Method and apparatus for sequence determination, device and storage medium

ABSTRACT

The present disclosure provides a method and an apparatus for sequence determination, a device and a storage medium. The method for sequence determination includes: mapping a first bit sequence having a length of K bits to a specified position based on M_index to obtain a second bit sequence; applying Polar encoding to the second bit sequence to obtain a Polar encoded bit sequence; and selecting T bits based on the Polar encoded bit sequence as a bit sequence to be transmitted, where K and T are both non-negative integers and K≤T.

CROSS REFERENCE TO RELATED APPLICATIONS

The present disclosure claims priorities to Chinese Patent ApplicationNo. 201710314013.X, filed on May 5, 2017, and Chinese Patent ApplicationNo. 201710737955.9, filed on Aug. 24, 2017, the content of which isincorporated herein by reference in its entirety.

TECHNICAL FIELD

The present disclosure relates to communication technology, and moreparticularly, to a method and an apparatus for sequence determination, adevice and a storage medium.

BACKGROUND

Due to the presence of channel noise, a channel coding, as anindependent part of a mobile communication system, guarantees thereliability, accuracy and effectiveness of information delivery.

Polar coding is a constructive coding scheme that has been strictlyproven to be capable of reaching a channel capacity. Polar code iscapable of satisfying requirements of the 5^(th) Generation (5G) NewRadio Access Technology (RAT) with respect to communication throughputand latency. A codeword encoded by Polar code can be represented asx=u·G_(N), where u=(u1, . . . , uN) is composed of information bits,known bits and parity check bits, G_(N)=F₂ ^(⊗n), F₂ ^(⊗n) denotes then-th Kronecker product of F₂,

${F_{2} = \begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}},$

and n=log 2(N).

Due to the Polarization characteristics of the Polar codes, input bitshave different reliabilities, i.e., input bits at different positionshave different Bit Error Rates (BERs). In order to improve a decodingperformance, the information bits and the parity check bits are placedat positions having high reliabilities (i.e., positions having low BERs)and the known bits are placed at positions having low reliabilities inan encoding process, such that the Block Error Rate (BLER) can beeffectively reduced.

Conventionally, for different mother code lengths of Polar codes,different hardware implementations would be required for permutation andrate matching of the information bits, parity check bits and known bits,which is highly complicated.

Currently, there are no effective solutions to the above problem in therelated art.

SUMMARY

The embodiments of the present disclosure provide a method and anapparatus for sequence determination, a device and a storage medium,capable of solving the problem in the related art associated with lackof a sequence determination scheme in the 5G New RAT.

According to an embodiment of the present disclosure, a method forsequence determination is provided. The method includes: mapping a firstbit sequence having a length of K bits to a position based on M_index toobtain a second bit sequence; applying Polar encoding to the second bitsequence to obtain a Polar encoded bit sequence; and selecting T bitsbased on the Polar encoded bit sequence as a bit sequence to betransmitted, where K and T are both non-negative integers and K≤T.

In an embodiment of the present disclosure, the method further includes,prior to mapping the first bit sequence having the length of K bits tothe specified position based on M_index to obtain the second bitsequence: applying a first predetermined transform to a first indexmatrix to obtain a second index matrix and obtaining M_index based onthe second index matrix. The first predetermined transform includes rowpermutation or column permutation.

In an embodiment of the present disclosure, the method further includes,prior to selecting T bits from the Polar encoded bit sequence as the bitsequence to be transmitted: forming a first bit sequence matrix based onthe Polar encoded bit sequence; and applying a second predeterminedtransform to the first bit sequence matrix to obtain a second bitsequence matrix. The second predetermined transform includes rowpermutation or column permutation. The operation of selecting T bitsbased on the Polar encoded bit sequence as the bit sequence to betransmitted includes: selecting T bits based on the second bit sequencematrix as the bit sequence to be transmitted.

In an embodiment of the present disclosure, the second index matrix isM_(re), which is a matrix of R_(re) rows and C_(re) columns. The firstindex matrix is M_(or), which is:

$M_{or} = {\quad{{{\begin{bmatrix}0 & 1 & 2 & \ldots & {C_{re} - 1} \\C_{re} & {C_{re} + 1} & {C_{re} + 2} & \ldots & {{2C_{re}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{\left( {R_{re} - 1} \right) \times C_{re}} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 1} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 2} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}\mspace{14mu} {or}\mspace{20mu} M_{or}} = \begin{bmatrix}0 & R_{re} & {2R_{re}} & \ldots & {\left( {C_{re} - 1} \right) \times R_{re}} \\1 & {R_{re} + 1} & {{2R_{re}} + 1} & \ldots & {{\left( {C_{re} - 1} \right) \times R_{re}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{R_{re} - 1} & {{2R_{re}} - 1} & {{3R_{re}} - 1} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}},}}$

where R_(re)×C_(re)≥N, R_(re) and C_(re) are both non-negative integers,and N is a length of the Polar encoded bit sequence.

In an embodiment of the present disclosure, when R_(re) is constant,C_(re) is a minimum value satisfying R_(re)×C_(re)≥N; or when C_(re) isconstant, R_(re) is a minimum value satisfying R_(re)×C_(re)≥N.

In an embodiment of the present disclosure, the operation of applyingthe first predetermined transform to the first index matrix to obtainthe second index matrix includes at least one of: the i-th column ofM_(re) being obtained from the π₁(i)-th column of M_(or) by means ofcolumn permutation, where 0≤i≤C_(re)−1, 0≤π₁(i)≤C_(re)−1,R_(re)×C_(re)≥N, and i and π₁(i) are both non-negative integers; or thej-th row of M_(re) being obtained from the π₂(j)-th row of M_(or), where0≤j≤R_(re)−1, 0≤π₂(j)≤R_(re)−1, R_(re)×C_(re)≥N, and j and π₂(j) areboth non-negative integers.

In an embodiment of the present disclosure, π₁(i) is obtained as atleast one of: π₁(i)=BRO(i), where BRO( ) denotes a bit reverse orderingoperation which includes: converting a decimal number i into a firstbinary number (B_(n1-1), B_(n1-2), . . . , B₀), reversing the firstbinary number to obtain a second binary number (B₀, B₁, . . . ,B_(n1-1)) and converting the second binary number into a decimal numberπ₁(i), where n1=log₂(C_(re)) and 0≤i≤C_(re)−1; i(i)={S1, S2, S3}, whereS1={0, 1, . . . , i1−1}, S2={i2, i3, i2+1, i3+1, . . . , i4, i5}, and S3is a set of elements in {0, 1, . . . , C_(re)−1} other than thoseincluded in S1 and S2, where C_(re)/8≤i1≤i2≤C_(re)/3,i2≤i4≤i3≤2C_(re)/3, i3≤i5≤C_(re)−1, i1, i2, i3, i4 and i5 are allnon-negative integers, and an intersection of any two of S1, S2 and S3is null; or π₁(i)={I}, where {I} is a sequence obtained by organizingnumerical results of applying a function f(r) to column indices r ofM_(or) in ascending or descending order, where 0≤r≤C_(re)−1.

In an embodiment of the present disclosure, f(r) includes at least oneof:

${{{f(r)} = {\sum_{{m1} = 0}^{{n1} - 1}{B_{m1} \times 2^{\frac{m1}{k}}}}},}\;$

(B_(n1-1), B_(n1-2), . . . , B₀) is a binary representation of the indexr, where 0≤m1≤n1−1, n1=log₂(C_(re)), and k is a non-negative integer;initializing a function value corresponding to r as f₁ ^((r)), andobtaining a function value for each element f_(C) _(re) ^((r)) aftern1-th iteration in accordance with a first iteration equation:

$\left\{ {\begin{matrix}{f_{2{m2}}^{({{2r} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m2}^{(r_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m2}^{(r_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2{m2}}^{({2r})} = {f_{m2}^{(r_{1})} + f_{m2}^{(r_{2})}}}\end{matrix},} \right.$

where f₁ ^((r)) is a mean log likelihood ratio; or initializing afunction value corresponding to r as f₁ ^((r)), and obtaining a functionvalue for each element f_(C) _(re) ^((r)) after n1-th iteration inaccordance with a second iteration equation:

$\left\{ {\begin{matrix}{f_{2{m3}}^{({{2r} - 1})} = {f_{m3}^{(r_{1})} + f_{m3}^{(r_{2})} - {f_{m3}^{(r_{1})}f_{m3}^{(r_{2})}}}} \\{f_{2{m3}}^{({2r})} = {f_{m3}^{(r_{1})}f_{m3}^{(r_{2})}}}\end{matrix},} \right.$

where f₁ ^((r)) is mutual information, where 1≤m2≤n1, 1≤m3≤n1, and r1,r2, 2r and 2r−1 are all integers larger than or equal to 0 and smallerthan or equal to C_(re)−1.

In an embodiment of the present disclosure, π₂(j) is obtained as atleast one of: π₂(j)=BRO(j), where BRO( ) denotes a bit reverse orderingoperation which includes: converting a decimal number j into a thirdbinary number (B_(n2-1), B_(n2-2), . . . , B₀), reversing the thirdbinary number to obtain a fourth binary number (B₀, B₁, . . . ,B_(n2-1)) and converting the fourth binary number into a decimal numberπ₂(j), where n2=log₂(R_(re)) and 0≤j≤R_(re)−1; λ₂(j)={S4, S5, S6}, whereS4={0, 1, . . . , j1−1}, S5={j2, j3, j2+1, j3+1, . . . , j4, j5}, and S6is a set of elements in {0, 1, . . . , R_(re)−1}other than thoseincluded in S4 and S5, where R_(re)/8≤j1≤j2≤R_(re)/3, j2≤j4≤j3≤2R_(re)/3, j3≤j5≤R_(re)−1, j1, j2, j3, j4 and j5 are all non-negativeintegers, and an intersection of any two of S4, S5 and S6 is null; orπ₂(j)={J}, where {J} is a sequence obtained by organizing numericalresults of applying a function f(s) to row indices s of M_(or) inascending or descending order, where 0≤s≤R_(re)−1.

In an embodiment of the present disclosure, f(s) includes at least oneof:

${{f(s)} = {\sum_{{m4} = 0}^{{n2} - 1}\; {B_{m4} \times 2^{\frac{m4}{k}}}}},$

(B_(n2-1), B_(n2-2), . . . , B₀) is a binary representation of the indexs, where 0≤m4≤n2−1, n2=log₂(R_(re)), and k is a non-negative integer;initializing a function value corresponding to s as f₁ ^((s)), andobtaining a function value for each element f_(R) _(re) ^((s)) aftern2-th iteration in accordance with a third iteration equation:

$\left\{ {\begin{matrix}{f_{2{m5}}^{({{2s} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m5}^{(s_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m5}^{(s_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2{m5}}^{({2s})} = {f_{m5}^{(s_{1})} + f_{m5}^{(s_{2})}}}\end{matrix},} \right.$

where f₁ ^((s)) is a mean log likelihood ratio; or initializing afunction value corresponding to s as f₁ ^((s)), and obtaining a functionvalue for each element f_(R) _(re) ^((s)) after n2-th iteration inaccordance with a fourth iteration equation:

$\left\{ {\begin{matrix}{f_{2{m6}}^{({{2s} - 1})} = {f_{m6}^{(s_{1})} + f_{m6}^{(s_{2})} - {f_{m6}^{(s_{1})}f_{m6}^{(s_{2})}}}} \\{f_{2{m6}}^{({2s})} = {f_{m6}^{(s_{1})}f_{m6}^{(s_{2})}}}\end{matrix},} \right.$

where f₁ ^((s)) is mutual information, where 1≤m5≤n2, 1≤m6≤n2, s1, s2,2s and 2s−1 are all integers larger than or equal to 0 and smaller thanor equal to R_(re)−1.

In an embodiment of the present disclosure, the first bit sequencematrix is M_(og). The second bit sequence matrix is M_(vb), which is amatrix of R_(vb) rows and C_(vb) columns. M_(og) is:

${M_{og} = {\left\lbrack \begin{matrix}x_{0} & x_{1} & x_{2} & \ldots & x_{C_{vb} - 1} \\x_{C_{vb}} & x_{C_{vb} + 1} & x_{C_{vb} + 2} & \ldots & x_{{2C_{vb}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{{({R_{vb} - 1})} \times C_{vb}} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 1} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 2} & \cdots & x_{{R_{vb} \times C_{vb}} - 1}\end{matrix} \right\rbrack \mspace{14mu} {or}}}$${{M_{og} = \begin{bmatrix}x_{0} & x_{R_{vb}} & x_{2R_{vb}} & \ldots & x_{{({C_{vb} - 1})} \times R_{vb}} \\x_{1} & x_{R_{vb} + 1} & x_{{2R_{vb}} + 1} & \ldots & x_{{{({C_{vb} - 1})} \times R_{vb}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{R_{vb} - 1} & x_{{2R_{vb}} - 1} & x_{{3R_{vb}} - 1} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}},}$

where x₀, x₁, x₂, . . . , x_(R) _(vb) _(×C) _(vb) ₋₁ is the Polarencoded bit sequence, R_(vb)×C_(vb)≥N, R_(vb) and C_(vb) are bothnon-negative integers and N is a length of the Polar encoded bitsequence.

In an embodiment of the present disclosure, when R_(vb) is constant,C_(vb) is a minimum value satisfying R_(vb)×C_(vb)≥N; or when C_(vb) isconstant, R_(vb) is a minimum value satisfying R_(vb)×C_(vb)≥N.

In an embodiment of the present disclosure, the operation of applyingthe second predetermined transform to the first bit sequence matrix toobtain the second bit sequence matrix includes at least one of: the g-thcolumn of M_(vb) being obtained from the π₃(g)-th column of M_(og) bymeans of column permutation, where 0≤g≤C_(vb)−1, 0≤π₃(g)≤C_(vb)−1,R_(vb)×C_(vb)≥N, and g and π₃(g) are both non-negative integers; or theh-th row of M_(vb) being obtained from the π₄(h)-th row of M_(og) bymeans of row permutation, where 0≤h≤R_(vb)−1, 0≤π₄(h)≤R_(vb)−1,R_(vb)×C_(vb)≥N, and h and π₄(h) are both non-negative integers.

In an embodiment of the present disclosure, π₃(g) is obtained as atleast one of: π₃(g)=BRO(g), where BRO( ) denotes a bit reverse orderingoperation which includes: converting a decimal number g into a fifthbinary number (B_(n3-1), B_(n3-2), . . . , B₀), reversing the fifthbinary number to obtain a sixth binary number (B₀, B₁₁, . . . ,B_(n3-1)) and converting the sixth binary number into a decimal numberπ₃(g), where n3=log₂(C_(vb)) and 0≤g≤C_(vb)−1; π₃(g)={S1, S2, S3}, whereS1={0, 1, . . . , g1−1}, S2={g2, g3, g2+1, g3+1, . . . , g4, g5}, and S3is a set of elements in {0, 1, . . . , C_(vb)−1)} other than thoseincluded in S1 and S2, where C_(vb)/8≤g1≤g2≤C_(vb)/3,g2≤g4≤g3≤2C_(vb)/3, g3≤g5≤C_(vb)−1, g1, g2, g3, g4 and g5 are allnon-negative integers, and an intersection of any two of S1, S2 and S3is null; π₃(g)={G}, where {G} is a sequence obtained by organizingnumerical results of applying a function f(α) to column indices α ofM_(og) in ascending or descending order, where 0≤α≤C_(vb)−1; π₃(g)={Q1,Q2, Q3}, where Q2={q1, q2, q1+1, q2+1, . . . , q3, q4},0≤q1≤q3≤(C_(vb)−1)/2, 0≤q2≤q4≤(C_(vb)−1)/2, q1, q2, q3, q4 and q5 areall non-negative integers, Q1 and Q3 are other elements in a differenceset between {0, 1, . . . , C_(vb)−1} and Q2, and an intersection of anytwo of Q1, Q2 and Q3 is null; π₃(g) being different from a predefinedsequence V1 in nV1 positions, where V1={0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 16, 13, 17, 14, 18, 15, 19, 20, 24, 21, 22, 25, 26, 28, 23,27, 29, 30, 31}, 0≤nV1≤23; or π₃(g) being different from a predefinedsequence V2 in nV2 positions, where V2={0, 1, 2, 4, 3, 5, 6, 7, 8, 16,9, 17, 10, 18, 11, 19, 12, 20, 13, 21, 14, 22, 15, 23, 24, 25, 26, 28,27, 29, 30, 31}, 0≤nV2≤3.

In an embodiment of the present disclosure, f(α) includes at least oneof:

${{f(\alpha)} = {\sum_{{m6} = 0}^{{n3} - 1}\; {B_{m6} \times 2^{\frac{m6}{k}}}}},$

(B_(n3-1), B_(n3-2), . . . , B₀) is a binary representation of the indexα, where 0≤m6≤n3−1, n3=log₂(C_(vb)), and k is a non-negative integer;initializing a function value corresponding to α as f₁ ^((α)), andobtaining a function value for each element f_(C) _(vb) ^((α)) aftern3-th iteration in accordance with a fifth iteration equation:

$\left\{ {\begin{matrix}{f_{2{m7}}^{({{2\alpha} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m7}^{(\alpha_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m7}^{(\alpha_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2{m7}}^{({2\alpha})} = {f_{m7}^{(\alpha_{1})} + f_{m7}^{(\alpha_{2})}}}\end{matrix},} \right.$

where f₁ ^((α)) is a mean log likelihood ratio; or initializing afunction value corresponding to s as f₁ ^((α)), and obtaining a functionvalue for each element f_(C) _(vb) ^((α)) after n3-th iteration inaccordance with a sixth iteration equation:

$\left\{ {\begin{matrix}{f_{2{m8}}^{({{2\alpha} - 1})} = {f_{m8}^{(\alpha_{1})} + f_{m8}^{(\alpha_{2})} - {f_{m8}^{(\alpha_{1})}f_{m8}^{(\alpha_{2})}}}} \\{f_{2{m8}}^{({2\alpha})} = {f_{m8}^{(\alpha_{1})}f_{m8}^{(\alpha_{2})}}}\end{matrix},} \right.$

where f₁ ^((α)) is mutual information, where 1≤m7≤n3, 1≤m8≤n3, and α1,α2, 2a and 2α−1 are all integers larger than or equal to 0 and smallerthan or equal to C_(vb)−1.

In an embodiment of the present disclosure, π₄(h) is obtained as atleast one of: π₄(h)=BRO(h), where BRO( ) denotes a bit reverse orderingoperation which includes: converting a decimal number h into a seventhbinary number (B_(n4-1), B_(n4-2), . . . , B₀), reversing the seventhbinary number to obtain an eighth binary number (B₀, B₁, . . . ,B_(n4-1)) and converting the eighth binary number into a decimal numberπ₄(h), where n4=log₂(R_(vb)) and 0≤h≤R_(vb)−1; π₄(h)={S4, S5, S6}, whereS4={0, 1, . . . , h1−1}, S5={h2, h3, h2+1, h3+1, . . . , h4, h5}, and S6is a set of elements in {0, 1, . . . , R_(vb)−1} other than thoseincluded in S4 and S5, where R_(vb)/8≤h1≤h2≤R_(vb)/3,h2≤h4≤h3≤2R_(vb)/3, h3≤h5≤R_(vb)−1, h1, h2, h3, h4 and h5 are allnon-negative integers, and an intersection of any two of S4, S5 and S6is null; π₄(h)={H}, where {H} is a sequence obtained by organizingnumerical results of applying a function f(β) to row indices β of M_(og)in ascending or descending order, where 0≤β≤R_(vb)−1; π₄(h)={O1, O2,O3}, where O2={o1, o2, o1+1, o2+1, . . . , o3, o4},0≤o1≤o3≤(R_(vb)−1)/2, 0≤o2≤o4≤(R_(vb)−1)/2, o1, o2, o3, o4 and o5 areall non-negative integers, O1 and O3 are other elements in a differenceset between {0, 1, . . . , R_(vb)−1} and O2, and an intersection of anytwo of O1, O2 and O3 is null; π₄(h) being different from a predefinedsequence VV1 in nVV1 positions, where VV1={0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 16, 13, 17, 14, 18, 15, 19, 20, 24, 21, 22, 25, 26, 28, 23,27, 29, 30, 31)}, 0≤nVV1≤23; or π₄(h) being different from a predefinedsequence VV2 in nVV2 positions, where VV2={0, 1, 2, 4, 3, 5, 6, 7, 8,16, 9, 17, 10, 18, 11, 19, 12, 20, 13, 21, 14, 22, 15, 23, 24, 25, 26,28, 27, 29, 30, 31}, 0≤nVV2≤3.

In an embodiment of the present disclosure, f(β) includes at least oneof:

${{f(\beta)} = {\sum_{{m\; 9} = 0}^{{n\; 4} - 1}{B_{m\; 9} \times 2^{\frac{m\; 9}{k}}}}},$

(B_(n4-1), B_(n4-2), . . . , B₀) is a binary representation of the indexβ, where 0≤m9≤n4−1, n4=log₂(R_(vb)), and k is a non-negative integer;initializing a function value corresponding to β as f₁ ^((β)), andobtaining a function value for each element f_(R) _(vb) ^((β)) aftern4-th iteration in accordance with a seventh iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 10}^{({{2\beta} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 10}^{(\beta_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 10}^{(\beta_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 10}^{({2\beta})} = {f_{m\; 10}^{(\beta_{1})} + f_{m\; 10}^{(\beta_{2})}}}\end{matrix},} \right.$

where f₁ ^((β)) is a mean log likelihood ratio; or initializing afunction value corresponding to β as f₁ ^((β)), and obtaining a functionvalue for each element f_(R) _(vb) ^((β))) after n4-th iteration inaccordance with an eighth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 11}^{({{2\beta} - 1})} = {f_{m\; 11}^{(\beta_{1})} + f_{m\; 11}^{(\beta_{2})} - {f_{m\; 11}^{(\beta_{1})}f_{m\; 11}^{(\beta_{2})}}}} \\{f_{2m\; 11}^{({2\beta})} = {f_{m\; 11}^{(\beta_{1})}f_{m\; 11}^{(\beta_{2})}}}\end{matrix},} \right.$

where f₁ ^((β)) is mutual information, where 1≤m10≤n4, 1≤m11≤n4, and β1,β2, 2β and 2β−1 are all integers larger than or equal to 0 and smallerthan or equal to R_(vb)−1.

In an embodiment of the present disclosure, the operation of obtainingM_index based on the second index matrix includes: selecting apredetermined number of indices from M_(re) row by row, column by columnor diagonal by diagonal, as M_index.

In an embodiment of the present disclosure, the operation of selectingthe predetermined number of indices from M_(re) column by columnincludes: selecting π_(p) indices from the p-th column of M_(re), whereΣ_(p=1) ^(C) ^(re) K_(p)=K, p is an integer, and 1≤p≤C_(re). Theoperation of selecting the predetermined number of indices from M_(re)row by row includes: selecting π_(q) indices from the q-th row ofM_(re), where Σ_(q=1) ^(R) ^(re) K_(q)=K, q is an integer, and1≤q≤R_(re). The operation of selecting the predetermined number ofindices from M_(re) diagonal by diagonal includes: selecting K_(δ)indices from the δ-th diagonal of M_(re), where

${{\sum_{\delta = {{- {\min {({R_{re},C_{re}})}}} + 1}}^{{\max {({R_{re},C_{re}})}} - 1}K_{\delta}} = K},$

δ is an integer, and −min(R_(re), C_(re))+1≤δ≤max(R_(re), C_(re))−1,where min(R_(re), C_(re)) denotes the smaller of R_(re) and C_(re), andmax(R_(re), C_(re)) denotes the larger of R_(re) and C_(re).

In an embodiment of the present disclosure, the operation of selectingthe predetermined number of indices from M_(re) column by columnincludes at least one of: selecting K_(ic1) indices from the 1^(st),2^(nd), C₁-th columns of M_(re), where Σ_(ic1=1) ^(C) ¹ K_(ic1)=K,1≤ic1≤C₁, 1≤C₁≤C_(re), and ic1 and C₁ are integers; selecting K_(ic2)indices from the C₂-th, (C₂+1)-th, . . . , C₃-th columns of M_(re),where Σ_(ic2=C) ₂ ^(C) ³ K_(ic2)=K, C₂≤ic2≤C₃, 1C₂≤C₃≤C_(re), and ic2,C₂ and C₃ are integers; or selecting K_(ic3) indices from the C₄-th,(C₄+1)-th, . . . , C_(re)-th columns of M_(re), where Σ_(ic3=C) ₄ ^(C)^(re) K_(ic3)=K, C₄≤ic3≤C_(re), 1≤C₄≤C_(re), and ic3 and C₄ areintegers.

In an embodiment of the present disclosure, the operation of selectingthe predetermined number of indices from M_(re) row by row includes atleast one of: selecting K_(ir1) indices from the 1^(st), 2^(nd), . . . ,R₁-th rows of M_(re), where Σ_(ir1=1) ^(R) ¹ K_(ir1)=K, 1≤ir1≤R₁,1≤R₁≤R_(re), and ir1 and R₁ are integers; selecting K_(ir2) indices fromthe R₂-th, (R₂+1)-th, . . . , R₃-th rows of M_(re), where Σ_(ir2=R) ₂^(R) ³ K_(ir2)=K, R₂≤ir2≤R₃, 1≤R₂≤R₃≤R_(re), and ir2, R₂ and R₃ areintegers; or selecting K_(ir3) indices from the R₄-th, (R₄+1)-th, . . ., R_(re)-th rows of M_(re), where Σ_(ir3=R) ₄ ^(R) ^(re) K_(p)=K,1≤R₄≤R_(re), and ir3 and R₄ are integers.

In an embodiment of the present disclosure, the operation of selectingthe predetermined number of indices from M_(re) diagonal by diagonalincludes at least one of: selecting K_(id1) indices from the(−min(R_(re), C_(re))+1)-th, (−min(R_(re), C_(re))+2)-th, . . . , D₁-thdiagonals of M_(re), where Σ_(id1=−min(R) _(re) _(, C) _(re) ₎₊₁ ^(D) ¹K_(id1)=K, −min(R_(re), C_(re))+1≤D₁≤max(R_(re), C_(re))−1, and id1 andD₁ are integers; selecting K_(id2) indices from the D₂-th, (D₂+1)-th, .. . , D₃-th diagonals of M_(re), where Σ_(id2=D) ₂₁ ^(D) ³ K_(id2)=K,−min(R_(re), C_(re))+1≤D₂≤D₃≤max(R_(re), C_(re))−1, and id2, D₂ and D₃are integers; and selecting K_(id3) indices from the D₄-th, (D₄+1)-th, .. . , (max(R_(re), C_(re))−1)-th diagonals of M_(re), where

${{\sum_{{{id}\; 3} = D_{4}}^{{\max {({R_{re},C_{re}})}} - 1}K_{{id}\; 3}} = K},$

−min(R_(re), C_(re))+1≤D₄≤max(R_(re), C_(re))−1, and id3 and D₄ areintegers, where min(R_(re), C_(re)) denotes the smaller of R_(re) andC_(re), and max(R_(re), C_(re)) denotes the larger of R_(re) and C_(re).

In an embodiment of the present disclosure, when the predeterminednumber of indices are selected from M_(re) row by row, column by columnor diagonal by diagonal, each index corresponding to a non-transmittedbit sequence in a second bit sequence matrix is skipped. The second bitsequence matrix is obtained from a first bit sequence matrix by using asecond predetermined transform. The first bit sequence matrix is formedfrom the Polar encoded bit sequence. The second predetermined transformincludes row permutation or column permutation.

In an embodiment of the present disclosure, the operation of selecting Tbits based on the second bit sequence matrix as the bit sequence to betransmitted includes: selecting T bits based on the second bit sequencematrix row by row, column by column or diagonal by diagonal, as the bitsequence to be transmitted.

In an embodiment of the present disclosure, the operation of selecting Tbits based on the second bit sequence matrix row by row, column bycolumn or diagonal by diagonal as the bit sequence to be transmittedincludes: selecting T bits based on the second bit sequence matrix rowby row, column by column or diagonal by diagonal, from a startingposition t in the second bit sequence matrix. When the selection reachesthe first or last bit in the second bit sequence matrix, it continueswith the last or first bit in the second bit sequence matrix, where1≤t≤R_(vb)×C_(vb).

In an embodiment of the present disclosure, the operation of selecting Tbits based on the second bit sequence matrix row by row, column bycolumn or diagonal by diagonal as the bit sequence to be transmittedincludes: selecting the 1^(st) to T-th bits or the (N−T+1)-th to N-thbits from the second bit sequence matrix column by column, when T issmaller than or equal to a length N of the Polar encoded bit sequence;selecting the 1^(st) to T-th bits or the (N−T+1)-th to N-th bits fromthe second bit sequence matrix row by row, when T is smaller than orequal to the length N of the Polar encoded bit sequence; selecting the1^(st) to T-th bits or the (N−T+1)-th to N-th bits from the second bitsequence matrix diagonal by diagonal, when T is smaller than or equal tothe length N of the Polar encoded bit sequence; selecting, when T islarger than the length N of the Polar encoded bit sequence, T bits rowby row, column by column or diagonal by diagonal, from the t-th bit inthe second bit sequence matrix. When the selection reaches the first orlast bit in the second bit sequence matrix, it continues with the lastor first bit in the second bit sequence matrix, where 1≤t≤R_(vb)×C_(vb)and N is a non-negative integer.

In an embodiment of the present disclosure, the operation of selecting Tbits from the second bit sequence matrix column by column includes atleast one of: selecting T_(ie1) bits from the 1^(st), 2^(nd), . . . ,E₁-th columns, where Σ_(ie1=1) ^(E) ¹ T_(ie1)=T, 1≤E₁≤C_(vb), and ie1and E₁ are integers; selecting T_(ie2) bits from the E₂-th, (E₂+1)-th, .. . , E₃-th columns, where Σ_(ie2=E) ₂ ^(E) ³ T_(ie2)=T, 1≤E₂≤E₃≤C_(re),and ie2, E₂ and E₃ are integers; or selecting T_(ie3) bits from theE₄-th, (E₄+1)-th, . . . E_(vb)-th columns, where Σ_(ie3=E) ₄ ^(C) ^(vb)T_(ie3)=T, 1≤E₄≤C_(vb), and ie3 and E₄ are integers.

In an embodiment of the present disclosure, the operation of selecting Tbits from the second bit sequence matrix row by row includes at leastone of: selecting Tin bits from the 1^(st), 2^(nd), . . . , F₁-th rows,where Σ_(if1=1) ^(F) ¹ T_(if1)=T, 1≤F₁≤R_(vb), and if1 and F₁ areintegers; selecting T_(if2) bits from the F₂-th, (F₂+1)-th, . . . ,F₃-th rows, where Σ_(if2=F) ₂ ^(F) ³ T_(if2)=T, 1≤F₂≤F₃≤R_(vb), and if2,F₂ and F₃ are integers; or selecting T_(if3) bits from the F₄-th,(F₄+1)-th, . . . , R_(vb)-th rows, where Σ_(if3=F) ₄ ^(R) ^(vb)T_(if3)=T, 1≤F₄≤R_(vb), and if3 and F₄ are integers.

In an embodiment of the present disclosure, the operation of selecting Tbits from the second bit sequence matrix diagonal by diagonal includesat least one of: selecting T_(ig1) bits from the (−min(R_(vb),C_(vb))+1)-th, (−min(R_(vb), C_(vb))+2)-th, . . . , G₁-th diagonals,where Σ_(ig1=−min(R) _(vb) _(, C) _(vb) ₎₊₁ ^(G) ¹ T_(ig1)=T,−min(R_(vb), C_(vb))+1≤G₁≤max(R_(vb), C_(vb))−1, and ig1 and G₁ areintegers; selecting K_(ig2) bits from the G₂-th, (G₂+1)-th, . . . ,G₃-th diagonals, where Σ_(ig2=G) ₂ ^(G) ³ T_(ig2)=T, −min(R_(vb),C_(vb))+1≤G₂≤G₃≤max(R_(vb), C_(vb))−1, and ig2, G₂ and G₃ are integers;or selecting K_(id3) bits from the G₄-th, (G₄+1)-th, . . . ,(max(R_(vb), C_(vb))−1)-th diagonals, where

${{{\sum_{{{ig}\; 3} = G_{4}}^{{\max {({R_{vb},C_{vb}})}} - 1}T_{{ig}\; 3}} = T},}\;$

−min(R_(vb), C_(vb))+1≤G₄≤max(R_(vb), C_(vb))−1, and ig3 and G₄ areintegers.

In an embodiment of the present disclosure, M_(og) has 32 columns.

According to an embodiment of the present disclosure, an apparatus forsequence determination is provided. The apparatus includes: a permutingmodule configured to map a first bit sequence having a length of K bitsto a specified position based on M_index to obtain a second bitsequence; an encoding module configured to apply Polar encoding to thesecond bit sequence to obtain a Polar encoded bit sequence; and aselecting module configured to select T bits based on the Polar encodedbit sequence as a bit sequence to be transmitted, where K and T are bothnon-negative integers and K≤T.

In an embodiment of the present disclosure, the apparatus furtherincludes: a first transform module configured to apply a firstpredetermined transform to a first index matrix to obtain a second indexmatrix and obtain M_index based on the second index matrix. The firstpredetermined transform includes row permutation or column permutation.

In an embodiment of the present disclosure, the apparatus furtherincludes: a second transform module configured to form a first bitsequence matrix from the Polar encoded bit sequence, and apply a secondpredetermined transform to the first bit sequence matrix to obtain asecond bit sequence matrix. The second predetermined transform includesrow permutation or column permutation. The selecting module is furtherconfigured to select T bits based on the second bit sequence matrix asthe bit sequence to be transmitted.

In an embodiment of the present disclosure, the second index matrix isM_(re), which is a matrix of R_(re) rows and C_(re) columns. The firstindex matrix is M_(or), which is:

$M_{or} = {\begin{bmatrix}0 & 1 & 2 & \ldots & {C_{re} - 1} \\C_{re} & {C_{re} + 1} & {C_{re} + 2} & \ldots & {{2C_{re}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{\left( {R_{re} - 1} \right) \times C_{re}} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 1} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 2} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}\mspace{14mu} {or}}$ ${M_{or} = \begin{bmatrix}0 & R_{re} & {2R_{re}} & \ldots & {\left( {C_{re} - 1} \right) \times R_{re}} \\1 & {R_{re} + 1} & {{2R_{re}} + 1} & \ldots & {{\left( {C_{re} - 1} \right) \times R_{re}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{R_{re} - 1} & {{2R_{re}} - 1} & {{3R_{re}} - 1} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}},$

where R_(re)×C_(re)≥N, R_(re) and C_(re) are both non-negative integers,and N is a length of the Polar encoded bit sequence.

In an embodiment of the present disclosure, when R_(re) is constant,C_(re) is a minimum value satisfying R_(re)×C_(re)≥N; or when C_(re) isconstant, R_(re) is a minimum value satisfying R_(re)×C_(re)≥N.

In an embodiment of the present disclosure, the first index matrix isconfigured such that the second index matrix is obtained according to atleast one of: the i-th column of M_(re) being obtained from the π₁(i)-thcolumn of M_(or) by means of column permutation, where 0≤i≤C_(re)−1,0≤π₁(i)≤C_(re)−1, R_(re)×C_(re)≥N, and i and π₁(i) are both non-negativeintegers; or the j-th row of M_(re) being obtained from the π₂(j)-th rowof M_(or), where 0≤j≤R_(re)−1, 0≤π₂(j)≤R_(re)−1, R_(re)×C_(re)≥N, and jand π₂(j) are both non-negative integers.

In an embodiment of the present disclosure, the first bit sequencematrix is M_(og). The second bit sequence matrix is M_(vb), which is amatrix of R_(vb) rows and C_(vb) columns. M_(og) is:

$M_{og} = {\begin{bmatrix}x_{0} & x_{1} & x_{2} & \ldots & x_{C_{vb} - 1} \\x_{C_{vb}} & x_{C_{vb} + 1} & x_{C_{vb} + 2} & \ldots & x_{{2C_{vb}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{{({R_{vb} - 1})} \times C_{vb}} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 1} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 2} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}\mspace{14mu} {or}}$$\mspace{20mu} {{M_{og} = \begin{bmatrix}x_{0} & x_{R_{vb}} & x_{2R_{vb}} & \ldots & x_{{({C_{vb} - 1})} \times R_{vb}} \\x_{1} & x_{R_{vb} + 1} & x_{{2R_{vb}} + 1} & \ldots & x_{{{({C_{vb} - 1})} \times R_{vb}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{R_{vb} - 1} & x_{{2R_{vb}} - 1} & x_{{3R_{vb}} - 1} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}},}$

where x₀, x₁, x₂, . . . , x_(R) _(vb) _(×C) _(vb) ₋₁ is the Polarencoded bit sequence, R_(vb)×C_(vb)≥N, R_(vb) and C_(vb) are bothnon-negative integers and N is a length of the Polar encoded bitsequence.

In an embodiment of the present disclosure, when R_(vb) is constant,C_(vb) is a minimum value satisfying R_(vb)×C_(vb)≥N; or when C_(vb) isconstant, R_(vb) is a minimum value satisfying R_(vb)×C_(vb)≥N.

In an embodiment of the present disclosure, the first bit sequencematrix is configured such that the second bit sequence matrix isobtained according to at least one of: the g-th column of M_(vb) beingobtained from the π₃(g)-th column of M_(og) by means of columnpermutation, where 0≤g≤C_(vb)−1, 0≤π₃(g)≤C_(vb)−1, R_(vb)×C_(vb)≥N, andg and π₃(g) are both non-negative integers; or the h-th row of M_(vb)being obtained from the π₄(h)-th row of M_(og) by means of rowpermutation, where 0≤h≤R_(vb)−1, 0≤π₄(h)≤R_(vb)−1, R_(vb)×C_(vb)≥N, andh and π₄(h) are both non-negative integers.

In an embodiment of the present disclosure, M_(og) has 32 columns.

According to an embodiment of the present disclosure, a device isprovided. The device includes: a processor configured to: map a firstbit sequence having a length of K bits to a specified position based onM_index to obtain a second bit sequence; apply Polar encoding to thesecond bit sequence to obtain a Polar encoded bit sequence; and select Tbits based on the Polar encoded bit sequence as a bit sequence to betransmitted, where K and T are both non-negative integers and K≤T, and amemory coupled to the processor.

In an embodiment of the present disclosure, the processor is furtherconfigured to: apply a first predetermined transform to a first indexmatrix to obtain a second index matrix; and obtain M_index based on thesecond index matrix. The first predetermined transform includes rowpermutation or column permutation.

In an embodiment of the present disclosure, the processor is furtherconfigured to: form a first bit sequence matrix from the Polar encodedbit sequence; apply a second predetermined transform to the first bitsequence matrix to obtain a second bit sequence matrix; and select Tbits based on the second bit sequence matrix as the bit sequence to betransmitted. The second predetermined transform includes row permutationor column permutation.

In an embodiment of the present disclosure, the second index matrix isM_(re), which is a matrix of R_(re) rows and C_(re) columns. The firstindex matrix is M_(or), which is:

$M_{or} = {\begin{bmatrix}0 & 1 & 2 & \ldots & {C_{re} - 1} \\C_{re} & {C_{re} + 1} & {C_{re} + 2} & \ldots & {{2C_{re}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{\left( {R_{re} - 1} \right) \times C_{re}} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 1} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 2} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}\mspace{14mu} {or}}$ ${M_{or} = \begin{bmatrix}0 & R_{re} & {2R_{re}} & \ldots & {\left( {C_{re} - 1} \right) \times R_{re}} \\1 & {R_{re} + 1} & {{2R_{re}} + 1} & \ldots & {{\left( {C_{re} - 1} \right) \times R_{re}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{R_{re} - 1} & {{2R_{re}} - 1} & {{3R_{re}} - 1} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}},$

where R_(re)×C_(re)≥N, R_(re) and C_(re) are both non-negative integers,and N is a length of the Polar encoded bit sequence.

In an embodiment of the present disclosure, when R_(re) is constant,C_(re) is a minimum value satisfying R_(re)×C_(re)≥N; or when C_(re) isconstant, R_(re) is a minimum value satisfying R_(re)×C_(re)≥N.

In an embodiment of the present disclosure, the processor is furtherconfigured to obtain the second index matrix according to at least oneof: the i-th column of M_(re) being obtained from the π₁(i)-th column ofM_(or) by means of column permutation, where 0≤i≤C_(re)−1,0≤π₁(i)≤C_(re)−1, R_(re)×C_(re)≥N, and i and π₁(i) are both non-negativeintegers; or the j-th row of M_(re) being obtained from the π₂(j)-th rowof M_(or), where 0≤j≤R_(re)−1, 0≤π₂(j)≤R_(re)−1, R_(re)×C_(re)≥N, and jand π₂(j) are both non-negative integers.

In an embodiment of the present disclosure, the first bit sequencematrix is M_(og). The second bit sequence matrix is M_(vb), which is amatrix of R_(vb) rows and C_(vb) columns. M_(og) is:

$M_{og} = {\begin{bmatrix}x_{0} & x_{1} & x_{2} & \ldots & x_{C_{vb} - 1} \\x_{C_{vb}} & x_{C_{vb} + 1} & x_{C_{vb} + 2} & \ldots & x_{{2C_{vb}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{{({R_{vb} - 1})} \times C_{vb}} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 1} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 2} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}\mspace{14mu} {or}}$$\mspace{20mu} {{M_{og} = \begin{bmatrix}x_{0} & x_{R_{vb}} & x_{2R_{vb}} & \ldots & x_{{({C_{vb} - 1})} \times R_{vb}} \\x_{1} & x_{R_{vb} + 1} & x_{{2R_{vb}} + 1} & \ldots & x_{{{({C_{vb} - 1})} \times R_{vb}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{R_{vb} - 1} & x_{{2R_{vb}} - 1} & x_{{3R_{vb}} - 1} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}},}$

where x₀, x₁, x₂, . . . , x_(R) _(vb) _(×C) _(vb) ₋₁ is the Polarencoded bit sequence, R_(vb)×C_(vb)≥N, R_(vb) and C_(vb) are bothnon-negative integers and N is a length of the Polar encoded bitsequence.

In an embodiment of the present disclosure, when R_(vb) is constant,C_(vb) is a minimum value satisfying R_(vb)×C_(vb)≥N; or when C_(vb) isconstant, R_(vb) is a minimum value satisfying R_(vb)×C_(vb)≥N.

In an embodiment of the present disclosure, the processor is configuredto obtain the second bit sequence matrix according to at least one of:the g-th column of M_(vb) being obtained from the π₃(g)-th column ofM_(og) by means of column permutation, where 0≤g≤C_(vb)−1,0≤π₃(g)≤C_(vb)−1, R_(vb)×C_(vb)≥N, and g and π₃(g) are both non-negativeintegers; or the h-th row of M_(vb) being obtained from the π₄(h)-th rowof M_(og) by means of row permutation, where 0≤h≤R_(vb)−1,0≤π₄(h)≤R_(vb)−1, R_(vb)×C_(vb)≥N, and h and π₄(h) are both non-negativeintegers.

In an embodiment of the present disclosure, M_(og) has 32 columns.

According to another embodiment of the present disclosure, a storagemedium is provided. The storage medium stores a program which, whenexecuted, performs the method according to any of the above embodiments.

According to yet another embodiment of the present disclosure, aprocessor is provided. The processor is configured to execute a programfor performing the method according to any of the above embodiments.

With the present disclosure, a first bit sequence having a length of Kbits is mapped to a specified position based on M_index to obtain asecond bit sequence. Polar encoding is applied to the second bitsequence to obtain a Polar encoded bit sequence. T bits are selectedbased on the Polar encoded bit sequence as a bit sequence to betransmitted. That is, the present disclosure provides a method fordetermining a bit sequence to be transmitted, capable of solving theproblem in the related art associated with lack of a sequencedetermination scheme in the 5G New RAT.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure can be further understood with reference to thefigures described below, which constitute a part of the presentdisclosure. The illustrative embodiments of the present disclosure anddescriptions thereof are provided for explaining, rather than limiting,the present disclosure. In the figures:

FIG. 1 is a block diagram showing a hardware structure of a mobileterminal in which a method for sequence determination can be appliedaccording to an embodiment of the present disclosure;

FIG. 2 is a flowchart illustrating a method for sequence determinationaccording to an embodiment of the present disclosure;

FIG. 3 is a block diagram showing a structure of an apparatus forsequence determination according to an embodiment of the presentdisclosure; and

FIG. 4 is a block diagram showing a structure of a device according toEmbodiment 3 of the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In the following, the present disclosure will be described in detailwith reference to the figures, taken in conjunction with theembodiments. The embodiments, and the features thereof, can be combinedwith each other, provided that they do not conflict.

It is to be noted that, the terms such as “first”, “second” and so on inthe description, claims and figures are used for distinguishing amongsimilar objects and do not necessarily imply any particularly order orsequence.

Embodiment 1

The method according to Embodiment 1 of the present disclosure can beperformed in a mobile terminal, a computer terminal or a similarcomputing device. When the method is performed in a mobile terminal forexample, FIG. 1 is a block diagram showing a hardware structure of amobile terminal in which a method for sequence determination can beapplied according to an embodiment of the present disclosure. As shownin FIG. 1, the mobile terminal 10 can include: one or more processors102 (only one is shown, including, but not limited to, a processingdevice such as a microprocessor or a Micro Control Unit (MCU) or aprogrammable logic device such as Field Programmable Gate Array (FPGA)),a memory 104 for storing data, and a transmission device 106 forproviding communication functions. It can be appreciated by thoseskilled in the art that the structure shown in FIG. 1 is illustrativeonly, and the structure of the above electronic device is not limitedthereto. For example, the mobile terminal 10 may include more or lesscomponents than those shown in FIG. 1, or have a different configurationfrom the one shown in FIG. 1.

The memory 104 can store software programs and modules of softwareapplications, e.g., program instructions/modules associated with themethod for sequence determination according to an embodiment of thepresent disclosure. The processor 102 performs various functionalapplications and data processing operations, i.e., performing the abovemethod, by executing the software programs and modules stored in thememory 104. The memory 104 may include a random cache or a non-volatilememory such as one or more magnetic storage devices, flash memories orother non-volatile solid-state memories. In some examples, the memory104 may further include one or more memories provided remotely from theprocessor 102, which can be connected to the mobile terminal 10 via anetwork. Examples of such network include, but not limited to, Internet,an intranet of an enterprise, a Local Area Network (LAN), a mobilecommunication network, or any combination thereof.

The transmission device 106 can transmit or receive data via a network.The network can be e.g., a wireless network provided by a communicationprovider of the mobile terminal 10. In an example, the transmissiondevice 106 includes a Network Interface Controller (NIC), which can beconnected to other network devices via a base station for communicationwith Internet. In an example, the transmission device 106 can be a RadioFrequency (RF) module for communicating with Internet wirelessly.

Alternatively, the method according to Embodiment 1 of the presentdisclosure can be, but not limited to be, performed in network device,e.g., a base station.

In this embodiment, a method performed in the above mobile terminal ornetwork device for sequence determination is provided. FIG. 2 is aflowchart illustrating a method for sequence determination according tothis embodiment. As shown in FIG. 2, the process includes the followingsteps.

At step S202, a first bit sequence having a length of K bits is mappedto a specified position based on M_index to obtain a second bitsequence.

At step S204, Polar encoding is applied to the second bit sequence toobtain a Polar encoded bit sequence.

At step S206, T bits are selected based on the Polar encoded bitsequence as a bit sequence to be transmitted, where K and T are bothnon-negative integers and K≤T.

With the above steps, a first bit sequence having a length of K bits ismapped to a specified position based on M_index to obtain a second bitsequence. Polar encoding is applied to the second bit sequence to obtaina Polar encoded bit sequence. T bits are selected based on the Polarencoded bit sequence as a bit sequence to be transmitted. That is, thepresent disclosure provides a method for determining a bit sequence tobe transmitted, capable of solving the problem in the related artassociated with lack of a sequence determination scheme in the 5G NewRAT.

It is to be noted that the above method may further include, prior tothe step S202: applying a first predetermined transform to a first indexmatrix to obtain a second index matrix and obtaining M_index based onthe second index matrix. The first predetermined transform includes rowpermutation or column permutation. That is, in the Polar encodingprocess, the same transform pattern is applied to one dimension of thefirst index matrix, such that only the other dimension of the firstindex matrix needs to be changed when a mother code length changes.Thus, the hardware can be reused in the implementation of Polar codes,thereby solving the problem in the related art associated withincapability of hardware reuse in the Polar encoding process.

It is to be noted that the method can further include, prior toselecting T bits based on the Polar encoded bit sequence as the bitsequence to be transmitted: forming a first bit sequence matrix from thePolar encoded bit sequence; and applying a second predeterminedtransform to the first bit sequence matrix to obtain a second bitsequence matrix. The second predetermined transform includes rowpermutation or column permutation. The operation of selecting T bitsbased on the Polar encoded bit sequence as the bit sequence to betransmitted includes: selecting T bits based on the second bit sequencematrix as the bit sequence to be transmitted. That is, the sametransform pattern is applied to one dimension of the first index matrix,such that only the other dimension of the first index matrix needs to bechanged when a mother code length changes. Thus, the hardware can befurther reused in the implementation of Polar codes, thereby furthersolving the problem in the related art associated with incapability ofhardware reuse in the Polar encoding process.

It is to be noted that the above method can further include, subsequentto applying the second predetermined transform to the first bit sequencematrix to obtain the second bit sequence matrix: storing bit sequencesin the second bit sequence matrix in a buffer and selecting T bits fromthe buffer as the bit sequence to be transmitted.

It is to be noted that the above buffer can be, but not limited to be,embodied as another physical or logic entity.

It is to be noted that the above first index matrix can be, but notlimited to, a two dimensional, three dimensional or multi-dimensionalmatrix. In an example where the above first index matrix is a twodimensional matrix, the above first predetermined transform can beembodied such that a row transform pattern or a column transform patternfor the first index matrix is the same.

In an example where the above first index matrix is a two dimensionalmatrix, in an embodiment of the present disclosure, the second indexmatrix is M_(re), which is a matrix of R_(re) rows and C_(re) columns.The first index matrix is M_(or), which is:

$M_{or} = {\begin{bmatrix}0 & 1 & 2 & \ldots & {C_{re} - 1} \\C_{re} & {C_{re} + 1} & {C_{re} + 2} & \ldots & {{2C_{re}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{\left( {R_{re} - 1} \right) \times C_{re}} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 1} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 2} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}\mspace{14mu} {or}}$ ${M_{or} = \begin{bmatrix}0 & R_{re} & {2R_{re}} & \ldots & {\left( {C_{re} - 1} \right) \times R_{re}} \\1 & {R_{re} + 1} & {{2R_{re}} + 1} & \ldots & {{\left( {C_{re} - 1} \right) \times R_{re}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{R_{re} - 1} & {{2R_{re}} - 1} & {{3R_{re}} - 1} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}},$

where R_(re)×C_(re)≥N, R_(re) and C_(re) are both non-negative integers,and N is a length of the Polar encoded bit sequence.

It is to be noted that the above R_(re) and C_(re) have one of thefollowing characteristics: when R_(re) is constant, C_(re) is a minimumvalue satisfying R_(re)×C_(re)≥N; or when C_(re) is constant, R_(re) isa minimum value satisfying R_(re)×C_(re)≥N.

It is to be noted that the operation of applying the first predeterminedtransform to the first index matrix to obtain the second index matrixincludes at least one of: the i-th column of M_(re) being obtained fromthe π₁(i)-th column of M_(or) by means of column permutation, where0≤i≤C_(re)−1, 0≤π₁(i)≤C_(re)−1, R_(re) C_(re)≥N, and i and π₁(i) areboth non-negative integers; or the j-th row of M_(re) being obtainedfrom the π₂(j)-th row of M_(or), where 0≤j≤R_(re)−1, 0≤π₂(j)≤R_(re)−1,R_(re)×C_(re)≥N, and j and π₂(j) are both non-negative integers.

In the Polar encoding process, as the permutation pattern from M_(or) toM_(re) is the same for each row, if the number of columns of each ofM_(or) and M_(re) is fixed, when the mother code length of the Polarcodes changes, only the number of rows of each of M_(or) and M_(re)needs to be changed. Alternatively, the permutation pattern from M_(or)to M_(re) can be the same for each column and, if the number of rows ofeach of M_(or) and M_(re) is fixed, when the mother code length of thePolar codes changes, only the number of columns of each of M_(or) andM_(re) needs to be changed. In this way, in the implementation of thePolar codes, if the hardware for mapping input bit sequences to inputpositions in the encoder is designed for the maximum mother code lengthN_(max), it also applies to situations where the mother code length issmaller than N_(max), which allows reuse of the hardware.

It is to be noted that the number of columns of the above M_(og) is 32.

It is to be noted that the above π₁(i) can be obtained according to atleast one of:

Scheme 1: π₁(i)=BRO(i), where BRO( ) denotes a bit reverse orderingoperation which includes: converting a decimal number i into a firstbinary number (B_(n1-1), B_(n1-2), . . . , B₀), reversing the firstbinary number to obtain a second binary number (B₀, B₁, . . . ,B_(n1-1)) and converting the second binary number into a decimal numberπ₁(i), where n1=log₂(C_(re)) and 0≤i≤C_(re)−1;

Scheme 2: π₁(i)={S1, S2, S3}, where S1={0, 1, . . . , i1−1}, S2={i2, i3,i2+1, i3+1, . . . , i4, i5}, and S3 is a set of elements in {0, 1, . . ., C_(re)−1} other than those included in S1 and S2, whereC_(re)/8≤i1≤i2≤C_(re)/3, i2≤i4≤i3≤2C_(re)/3, i3≤i5≤C_(re)−1, i1, i2, i3,i4 and i5 are all non- negative integers, and an intersection of any twoof S1, S2 and S3 is null; or

Scheme 3: π₁(i)={I}, where {I} is a sequence obtained by organizingnumerical results of applying a function f(r) to column indices r ofM_(or) in ascending or descending order, where 0≤r≤C_(re)−1.

The above three schemes will be explained with reference to thefollowing examples.

For Scheme 1, if C_(re)=8, i=6, then n1=log₂(8)=3. i=6 is converted intoa binary number (B₂, B₁, B₀)=(1, 1, 0). The binary number (B₂, B₁,B₀)=(1, 1, 0) is reversed to obtain (B₀, B₁, B₂)=(0, 1, 1). (B₀, B₁,B₂)=(0, 1, 1) is then converted into a decimal number π₁(i)=3.

For Scheme 2, if C_(re)=8, i₁=2, i₂=2, i₃=4, i₄=3 and i₅=5, then S1={0,1}, S2={2, 4, 3, 5}, S3={6, 7}, and π₁(i)={0, 1, 2, 4, 3, 5, 6, 7}.

For Scheme 3, C_(re)=8, {f(0), . . . , f(7)}={0, 1, 1.18, 2.18, 1.41,2.41, 2.60, 3.60}. f(0), . . . , f(7) is organized in ascending order toobtain 1 i(i)={1, 2, 3, 5, 4, 6, 7, 8}.

It is to be noted that f(r) includes at least one of:

${{f(r)} = {\sum_{{m\; 1} = 0}^{{n\; 1} - 1}{B_{m\; 1} \times 2^{\frac{m\; 1}{k}}}}},$

(B_(n1-1), B_(n1-2), . . . , B₀) is a binary representation of the indexr, where 0≤m1≤n1−1, n1=log₂(C_(re)), and k is a non-negative integer(e.g., C_(re)=8, i=6, k=4, n1=log₂(8)=3, i=6 is converted into a binarynumber (B₂, B₁, B₀)=(1, 1, 0),

${{f(6)} = {{\sum_{{m\; 1} = 0}^{{n\; 1} - 1}{B_{m\; 1} \times 2^{\frac{m\; 1}{4}}}} = {{{0 \times 2^{\frac{0}{4}}} + {1 \times 2^{\frac{1}{4}}} + {1 \times 2^{\frac{2}{4}}}} = 2.4142}}},$

where ( ) Σ is a summation equation);

initializing a function value corresponding to r as f₁ ^((r)), andobtaining a function value for each element f_(C) _(re) ^((r)) aftern1-th iteration in accordance with a first iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 2}^{({{2r} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 2}^{(r_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 2}^{(r_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 2}^{({2r})} = {f_{m\; 2}^{(r_{1})} + f_{m\; 2}^{(r_{2})}}}\end{matrix},} \right.$

where f₁ ^((r)) is a mean log likelihood ratio (e.g., φ(z) can beapproximately:

${\phi (z)} = \left\{ {\begin{matrix}{{1 - {\frac{1}{\sqrt{4{\pi z}}}{\int_{- \infty}^{+ \infty}{\tanh \frac{u}{2}{\exp \left( {{- \left( {u - z} \right)^{2}}/\left( {4z} \right)} \right)}{du}}}}}\ } & {z > 0} \\{1,{z = 0}} & \;\end{matrix},} \right.$

where the nodes i₁ and i₂ involving in the iterative calculation aredependent on the structure of the Polar encoder);

(Let the initial value f₁ ^((r))=2/σ², where σ² is the variance ofnoise, C_(re)=8, σ²=0. f₁ ^((r)) is substituted into the iterationequation to obtain f₂ ^((r)), which is then substituted into theiteration equation to obtain f₄ ^((r)), and so on, until f₈ ^((r)) iscalculated, where f(r)=f₈ ^((r)), 0≤r≤C_(re)−1, {f(0), . . . ,f(7)}={0.04, 0.41, 0.61, 3.29, 1.00, 4.56, 5.78, 16.00}); or

initializing a function value corresponding to r as f₁ ^((r)), andobtaining a function value for each element f_(C) _(re) ^((r)) aftern1-th iteration in accordance with a second iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 3}^{({{2r} - 1})} = {f_{m\; 3}^{(r_{1})} + f_{m\; 3}^{(r_{2})} - {f_{m\; 3}^{(r_{1})}f_{m\; 3}^{(r_{2})}}}} \\{f_{2m\; 3}^{({2r})} = {f_{m\; 3}^{(r_{1})}f_{m\; 3}^{(r_{2})}}}\end{matrix},} \right.$

where f₁ ^((r)) is mutual information, where 1≤m2≤n1, 1≤m3≤n1, and r1,r2, 2r and 2r−1 are all integers larger than or equal to 0 and smallerthan or equal to C_(re)−1 (the nodes i₁ and i₂ involving in theiterative calculation are dependent on the structure of the Polarencoder);

(Let f₁ ^((r))=0.5 and C_(re)=8. f₁ ^((r)) is substituted into theiteration equation to obtain f₂ ^((r)), which is then substituted intothe iteration equation to obtain f₄ ^((r)), and so on, until f₈ ^((r))is calculated, where f(r)=f₈ ^((r)), 0≤i≤C_(re)−1, {f(0), . . . ,f(7)}={0.008, 0.152, 0.221, 0.682, 0.313, 0.779, 0.850, 0.991}).

It is to be noted that the above π₂(j) can be obtained according to atleast one of:

π₂(j)=BRO(j), where BRO( ) denotes a bit reverse ordering operationwhich includes: converting a decimal number j into a third binary number(B_(n2-1), B_(n2-2), . . . , B₀), reversing the third binary number toobtain a fourth binary number (B₀, B₁, . . . , B_(n2-1)) and convertingthe fourth binary number into a decimal number π₂(j), wheren2=log₂(R_(re)) and 0≤j≤R_(re)−1;

π₂(j)={S4, S5, S6}, where S4={0, 1, . . . , j1−1}, S5={j2, j3, j2+1,j3+1, . . . , j4, j5}, and S6 is a set of elements in {0, 1, . . . ,R_(re)−1} other than those included in S4 and S5, whereR_(re)/8≤j1≤j2≤R_(re)/3, j2≤j4≤j3≤2 R_(re)/3, j3≤j5≤R_(re)−1, j1, j2,j3, j4 and j5 are all non- negative integers, and an intersection of anytwo of S4, S5 and S6 is null; or

π₂(j)={J}, where {J} is a sequence obtained by organizing numericalresults of applying a function f(s) to row indices s of M_(or) inascending or descending order, where 0≤s≤R_(re).

It is to be noted that f(s) includes at least one of:

${{f(s)} = {\sum_{{m\; 4} = 0}^{{n\; 2} - 1}{B_{m\; 4} \times 2^{\frac{m\; 4}{k}}}}},$

(B_(n2-1), B_(n2-2), . . . , B₀) is a binary representation of the indexs, where 0≤m4≤n2−1, n2=log₂(R_(re)), and k is a non-negative integer;

initializing a function value corresponding to s as f₁ ^((s)), andobtaining a function value for each element f_(R) _(re) ^((s)) aftern2-th iteration in accordance with a third iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 5}^{({{2s} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 5}^{(s_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 5}^{(s_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 5}^{({2s})} = {f_{m\; 5}^{(s_{1})} + f_{m\; 5}^{(s_{2})}}}\end{matrix},} \right.$

where f₁ ^((s)) is a mean log likelihood ratio; or

initializing a function value corresponding to s as f(s), and obtaininga function value for each element f_(R) _(re) ^((s)) by updating f₁^((s)) for n2 iterations in accordance with a fourth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 6}^{({{2s} - 1})} = {f_{m\; 6}^{(s_{1})} + f_{m\; 6}^{(s_{2})} - {f_{m\; 6}^{(s_{1})}f_{m\; 6}^{(s_{2})}}}} \\{f_{2m\; 6}^{({2s})} = {f_{m\; 6}^{(s_{1})}f_{m\; 6}^{(s_{2})}}}\end{matrix},} \right.$

where f₁ ^((s)) is mutual information, where 1≤m5≤n2, 1≤m6≤n2, s1, s2,2s and 2s−1 are all integers larger than or equal to 0 and smaller thanor equal to R_(re)−1.

It is to be noted that, for explanations for the above π₂(j), referencecan be made to π₁(i).

It is to be noted that the above first bit sequence matrix can be, butnot limited to, a two dimensional, three dimensional ormulti-dimensional matrix. In an example where the above first bitsequence matrix is a two dimensional matrix, the above secondpredetermined transform can be embodied such that a row transformpattern or a column transform pattern for the first bit sequence matrixis the same.

It is to be noted that the first bit sequence matrix is M_(og). Thesecond bit sequence matrix is M_(vb), which is a matrix of R_(vb) rowsand C_(vb) columns. M_(og) is:

$M_{og} = {\begin{bmatrix}x_{0} & x_{1} & x_{2} & \ldots & x_{C_{vb} - 1} \\x_{C_{vb}} & x_{C_{vb} + 1} & x_{C_{vb} + 2} & \ldots & x_{{2C_{vb}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{{({R_{vb} - 1})} \times C_{vb}} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 1} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 2} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}\mspace{14mu} {or}}$$\mspace{20mu} {\quad{{M_{og} = \begin{bmatrix}x_{0} & x_{R_{vb}} & x_{2R_{vb}} & \ldots & x_{{({C_{vb} - 1})} \times R_{vb}} \\x_{1} & x_{R_{vb} + 1} & x_{{2R_{vb}} + 1} & \ldots & x_{{{({C_{vb} - 1})} \times R_{vb}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{R_{vb} - 1} & x_{{2R_{vb}} - 1} & x_{{3R_{vb}} - 1} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}},}}$

where x₀, x₁, x₂, . . . , x_(R) _(vb) _(×C) _(vb) ₋₁ is the Polarencoded bit sequence, R_(vb)×C_(vb)≥N, R_(vb) and C_(vb) are bothnon-negative integers and N is a length of the Polar encoded bitsequence.

It is to be noted that when R_(vb) is constant, C_(vb) is a minimumvalue satisfying R_(vb)×C_(vb)≥N; or when C_(vb) is constant, R_(vb) isa minimum value satisfying R_(vb)×C_(vb)≥N.

It is to be noted that the operation of applying the secondpredetermined transform to the first bit sequence matrix to obtain thesecond bit sequence matrix can include at least one of: the g-th columnof M_(vb) being obtained from the π₃(g)-th column of M_(og) by means ofcolumn permutation, where 0≤g≤C_(vb)−1, 0≤π₃(g)≤C_(vb)−1,R_(vb)×C_(vb)≥N, and g and π₃(g) are both non-negative integers; or theh-th row of M_(vb) being obtained from the π₄(h)-th row of M_(og) bymeans of row permutation, where 0≤h≤R_(vb)−1, 0≤π₄(h)≤R_(vb)−1,R_(vb)×C_(vb)≥N, and h and π₄(h) are both non-negative integers.

In the encoding process, the process of selecting appropriate bits fromthe encoded bit sequence to form a bit sequence to be transmitted is arate matching process. In the Polar encoding process, as the permutationpattern from M_(og) to M_(vb) is the same for each row, if the number ofcolumns of each of M_(og) and M_(vb) is fixed, when the mother codelength of the Polar codes changes, only the number of rows of each ofM_(og) and M_(vb) needs to be changed. Alternatively, the permutationpattern from M_(og) to M_(vb) can be the same for each column and, ifthe number of rows of each of M_(og) and M_(vb) is fixed, when themother code length of the Polar codes changes, only the number ofcolumns of each of M_(og) and M_(vb) needs to be changed.

In this way, in the implementation of the Polar codes, if the hardwarefor mapping input bit sequences to input positions in the encoder isdesigned for the maximum mother code length N_(max), it also applies tosituations where the mother code length is smaller than N_(max), whichallows reuse of the hardware.

It is to be noted that π₃(g) can be obtained according to at least oneof:

π₃(g)=BRO(g), where BRO( ) denotes a bit reverse ordering operationwhich includes: converting a decimal number g into a fifth binary number(B_(n3-1), B_(n3-2), . . . , B₀), reversing the fifth binary number toobtain a sixth binary number (B₀, B₁₁, . . . , B_(n3-1)) and convertingthe sixth binary number into a decimal number π₃(g), wheren3=log₂(C_(vb)) and 0≤g≤C_(vb)−1;

π₃(g)={S1, S2, S3}, where S1={0, 1, . . . , g1−1}, S2={g2, g3, g2+1,g3+1, . . . , g4, g5}, and S3 is a set of elements in {0, 1, . . . ,C_(vb)−1} other than those included in S1 and S2, whereC_(vb)/8≤g1≤g2≤C_(vb)/3, g2≤g4≤g3≤2C_(vb)/3, g3≤g5≤C_(vb)−1, g1, g2, g3,g4 and g5 are all non- negative integers, and an intersection of any twoof S1, S2 and S3 is null;

π₃(g)={G}, where {G} is a sequence obtained by organizing numericalresults of applying a function f(α) to column indices α of M_(og) inascending or descending order, where 0≤α≤C_(vb)−1;

π₃(g)={Q1, Q2, Q3}, where Q2={q1, q2, q1+1, q2+1, . . . , q3, q4},0≤q1≤q3≤(C_(vb)−1)/2, 0≤q2≤q4≤(C_(vb)−1)/2, q1, q2, q3, q4 and q5 areall non-negative integers, Q1 and Q3 are other elements in a differenceset between {0, 1, . . . , C_(vb)−1} and Q2, and an intersection of anytwo of Q1, Q2 and Q3 is null;

π₃(g) being different from a predefined sequence V1 in nV1 positions,where V1={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 13, 17, 14, 18,15, 19, 20, 24, 21, 22, 25, 26, 28, 23, 27, 29, 30, 31}, 0≤nV1≤23; or

π₃(g) being different from a predefined sequence V2 in nV2 positions,where V2={0, 1, 2, 4, 3, 5, 6, 7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20,13, 21, 14, 22, 15, 23, 24, 25, 26, 28, 27, 29, 30, 31}, 0≤nV2≤3.

It is to be noted that f(α) includes at least one of:

${{f(\alpha)} = {\sum_{{m\; 6} = 0}^{{n\; 3} - 1}{B_{m\; 6} \times 2^{\frac{m\; 6}{k}}}}},$

(B_(n3-1), B_(n3-2), . . . , B₀) is a binary representation of the indexα, where 0≤m6≤n3−1, n3=log₂(C_(vb)), and k is a non-negative integer;

initializing a function value corresponding to α as f₁ ^((α)), andobtaining a function value for each element f_(C) _(vb) ^((α)) aftern3-th iteration in accordance with a fifth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 7}^{({{2\alpha} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 7}^{(\alpha_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 7}^{(\alpha_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 7}^{({2\alpha})} = {f_{m\; 7}^{(\alpha_{1})} + f_{m\; 7}^{(\alpha_{2})}}}\end{matrix},} \right.$

where f₁ ^((α)) is a mean log likelihood ratio; or

initializing a function value corresponding to s as f₁ ^((α)), andobtaining a function value for each element after n3-th iteration inaccordance with a sixth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 8}^{({{2\alpha} - 1})} = {f_{m\; 8}^{(\alpha_{1})} + f_{m\; 8}^{(\alpha_{2})} - {f_{m\; 8}^{(\alpha_{1})}f_{m\; 8}^{(\alpha_{2})}}}} \\{f_{2m\; 8}^{({2\alpha})} = {f_{m\; 8}^{(\alpha_{1})}f_{m\; 8}^{(\alpha_{2})}}}\end{matrix},} \right.$

where f₁ ^((α)) is mutual information, where 1≤m7≤n3, 1≤m8≤n3, and α1,α2, 2α and 2α−1 are all integers larger than or equal to 0 and smallerthan or equal to C_(vb)−1.

It is to be noted that π₄(h) can be obtained according to at least oneof:

π₄(h)=BRO(h), where BRO( ) denotes a bit reverse ordering operationwhich includes: converting a decimal number h into a seventh binarynumber (B_(n4-1), B_(n4-2), . . . , B₀), reversing the seventh binarynumber to obtain an eighth binary number (B₀, B₁, . . . , B_(n4-1)) andconverting the eighth binary number into a decimal number π₄(h), wheren4=log₂(R_(vb)) and 0≤h≤R_(vb)−1;

π₄(h)={S4, S5, S6}, where S4={0, 1, . . . , h1−1}, S5={h2, h3, h2+1,h3+1, . . . , h4, h5}, and S6 is a set of elements in {0, 1, . . . ,R_(vb)−1} other than those included in S4 and S5, whereR_(vb)/8≤h1≤h2≤R_(vb)/3, h2≤h4≤h3≤2R_(vb)/3, h3≤h5≤R_(vb)−1, h1, h2, h3,h4 and h5 are all non- negative integers, and an intersection of any twoof S4, S5 and S6 is null;

π₄(h)={H}, where {H} is a sequence obtained by organizing numericalresults of applying a function f(3) to row indices β of M_(og) inascending or descending order, where 0≤3≤R_(vb)−1;

π₄(h)={O1, O2, O3}, where O2={o1, o2, o1+1, o2+1, . . . , o3, o4},0≤o1≤o3≤(R_(vb)−1)/2, 0≤o2≤o4≤(R_(vb)−1)/2, o1, o2, o3, o4 and o5 areall non-negative integers, O1 and O3 are other elements in a differenceset between {0, 1, . . . , R_(vb)−1} and O2, and an intersection of anytwo of O1, O2 and O3 is null;

π₄(h) being different from a predefined sequence VV1 in nVV1 positions,where VV1={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 13, 17, 14, 18,15, 19, 20, 24, 21, 22, 25, 26, 28, 23, 27, 29, 30, 31}, 0≤nVV1≤23; or

π₄(h) being different from a predefined sequence VV2 in nVV2 positions,where VV2={0, 1, 2, 4, 3, 5, 6, 7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20,13, 21, 14, 22, 15, 23, 24, 25, 26, 28, 27, 29, 30, 31}, 0≤nVV2≤3.

It is to be noted that f(β) includes at least one of:

${{f(\beta)} = {\sum_{{m\; 9} = 0}^{{n\; 4} - 1}{B_{m\; 9} \times 2^{\frac{m\; 9}{k}}}}},$

(B_(n4-1), B_(n4-2), . . . , B₀) is a binary representation of the indexβ, where 0≤m9≤n4−1, n4=log₂(R_(vb)), and k is a non-negative integer;

initializing a function value corresponding to β as f₁ ^((β)), andobtaining a function value for each element f_(R) _(vb) ^((β)) aftern4-th iteration in accordance with a seventh iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 10}^{({{2\beta} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 10}^{(\beta_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 10}^{(\beta_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 10}^{({2\beta})} = {f_{m\; 10}^{(\beta_{1})} + f_{m\; 10}^{(\beta_{2})}}}\end{matrix},} \right.$

where is a mean log likelihood ratio; or

initializing a function value corresponding to β as f₁ ^((β)), andobtaining a function value for each element f_(R) _(vb) ^((β)) aftern4-th iteration in accordance with an eighth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 11}^{({{2\beta} - 1})} = {f_{m\; 11}^{(\beta_{1})} + f_{m\; 11}^{(\beta_{2})} - {f_{m\; 11}^{(\beta_{1})}f_{m\; 11}^{(\beta_{2})}}}} \\{f_{2m\; 11}^{({2\beta})} = {f_{m\; 11}^{(\beta_{1})}f_{m\; 11}^{(\beta_{2})}}}\end{matrix},} \right.$

where f₁ ^((β))is mutual information, where 1≤m10≤n4, 1≤m11≤n4, and β1,β2, 2β and 2β−1 are all integers larger than or equal to 0 and smallerthan or equal to R_(vb)−1.

It is to be noted that, for explanations for π₃(g) and π₄(h), referencecan be made to π₁(i) and descriptions thereof will be omitted here.

In an embodiment of the present disclosure, the operation of obtainingM_index based on the second index matrix includes: selecting apredetermined number of indices from M_(re) row by row, column by columnor diagonal by diagonal, as M_index.

In an embodiment of the present disclosure, the operation of selectingthe predetermined number of indices from M_(re) column by columnincludes: selecting π_(p) indices from the p-th column of M_(re), whereΣ_(p=1) ^(C) ^(re) K_(p)=K, p is an integer, and 1≤p≤C_(re). Theoperation of selecting the predetermined number of indices from M_(re)row by row includes: selecting π_(q) indices from the q-th row ofM_(re), where Σ_(q=1) ^(R) ^(re) K_(q)=K, q is an integer, and1≤q≤R_(re). The operation of selecting the predetermined number ofindices from M_(re) diagonal by diagonal includes: selecting K_(δ)indices from the δ-th diagonal of M_(re), where

${{\sum_{\delta = {{- {\min {({R_{re},C_{re}})}}} + 1}}^{{\max {({R_{re},C_{re}})}} - 1}K_{\delta}} = K},$

δ is an integer, and −min(R_(re), C_(re))+1≤δ≤max(R_(re), C_(re))−1,where min(R_(re), C_(re)) denotes the smaller of R_(re) and C_(re), andmax(R_(re), C_(re)) denotes the larger of R_(re) and C_(re).

In an embodiment of the present disclosure, the operation of selectingthe predetermined number of indices from M_(re) column by columnincludes at least one of: selecting K_(ic1) indices from the 1^(st),2^(nd), C₁-th columns of M_(re), where Σ_(ic1=1) ^(C) ¹ K_(ic1)=K,1≤ic1≤C₁, 1≤C₁≤C_(re), and ic1 and C₁ are integers; selecting K_(ic2)indices from the C₂-th, (C₂+1)-th, . . . , C₃-th columns of M_(re),where Σ_(ic2=C) ₂ ^(C) ³ K_(ic2)=K, C₂≤ic2≤C₃, 1≤C₂≤C₃≤C_(re), and ic2,C₂ and C₃ are integers; or selecting K_(ic3) indices from the C₄-th,(C₄+1)-th, . . . , C_(re)-th columns of M_(re), where Σ_(ic3=C) ₄ ^(C)^(re) K_(ic3)=K, C₄≤ic3≤C_(re), 1≤C₄≤C_(re), and ic3 and C₄ areintegers.

In an embodiment of the present disclosure, the operation of selectingthe predetermined number of indices from M_(re) row by row includes atleast one of: selecting K_(ir1) indices from the 1^(st), 2^(nd), . . . ,R₁-th rows of M_(re), where Σ_(ir1=1) ^(R) ¹ K_(ir1)=K, 1≤ir1≤R₁,1≤R₁≤R_(re), and ir1 and R₁ are integers; selecting K_(ir2) indices fromthe R₂-th, (R₂+1)-th, . . . , R₃-th rows of M_(re), where Σ_(ir2=R) ₂^(R) ³ K_(ir2)=K, R₂≤ir2≤R₃, 1≤R₂≤R₃≤R_(re), and ir2, R₂ and R₃ areintegers; or selecting K_(ir3) indices from the R₄-th, (R₄+1)-th, . . ., R_(re)-th rows of M_(re), where Σ_(ir3=R) ₄ ^(R) ^(re) K_(p)=K,1≤R₄≤R_(re), and ir3 and R₄ are integers.

In an embodiment of the present disclosure, the operation of selectingthe predetermined number of indices from M_(re) diagonal by diagonalincludes at least one of: selecting K_(id1) indices from the(−min(R_(re), C_(re))+1)-th, (−min(R_(re), C_(re))+2)-th, . . . , D₁-thdiagonals of M_(re), where Σ_(id1=−min(R) _(re) _(, C) _(re) ₎₊₁ ^(D) ¹K_(id1)=K, −min(R_(re), C_(re))+1≤D₁≤max(R_(re), C_(re))−1, and id1 andD₁ are integers; selecting K_(id2) indices from the D₂-th, (D₂+1)-th, .. . , D₃-th diagonals of M_(re), where Σ_(id2=D) ₂₁ ^(D) ³ K_(id2)=K,−min(R_(re), C_(re))+1≤D₂≤D₃≤max(R_(re), C_(re))−1, and id2, D₂ and D₃are integers; and selecting K_(id3) indices from the D₄-th, (D₄+1)-th, .. . , (max(R_(re), C_(re))−1)-th diagonals of M_(re), where

${{{\sum_{{{id}\; 3} = D_{4}}^{{\max {({R_{re},C_{re}})}} - 1}K_{{id}\; 3}} = K},}\;$

−min(R_(re), C_(re))+1≤D₄≤max(R_(re), C_(re))−1, and id3 and D₄ areintegers, where min(R_(re), C_(re)) denotes the smaller of R_(re) andC_(re), and max(R_(re), C_(re)) denotes the larger of R_(re) and C_(re).

It is to be noted that, for a matrix M as an example, if M is a squarematrix, the number, cc, of its columns is equal to the number, rr, ofits rows. If the 0-th diagonal is the primary diagonal, the diagonalsparallel with the primary diagonal are the 1^(st), 2^(nd), . . . ,(rr−1)-th diagonals from the bottom up, and the diagonals parallel withthe primary diagonal are the −1^(st), −2^(nd), . . . , (−rr+1)-thdiagonals from the top down. If the 0-th diagonal is the secondarydiagonal, the diagonals parallel with the secondary diagonal are the1^(st), 2^(nd), . . . , (rr−1)-th diagonals from the bottom up, and thediagonals parallel with the secondary diagonal are the −1^(st), −2^(nd),. . . , (−rr+1)-th diagonals from the top down.

It is to be noted that, for a matrix M as an example, if M is not asquare matrix, the number, cc, of its columns can be larger than thenumber, rr, of its rows. For the matrix

$\quad\begin{pmatrix}a_{1,1} & a_{1,2} & \ldots & a_{1,{cc}} \\a_{2,1} & a_{2,2} & \ldots & a_{2,{cc}} \\\vdots & \vdots & \ddots & \vdots \\a_{{rr},1} & a_{{rr},2} & \ldots & a_{{rr},{cc}}\end{pmatrix}$

as an example, if the 0-th diagonal is along the line connecting theelement a_(1,cc) and a_(rr,cc-rr+1), the diagonals parallel with the0-th diagonal are the 1^(st), 2^(nd), . . . , (rr−1)-th diagonals fromthe bottom up, and the diagonals parallel with the 0-th diagonal are the−1^(st), −2^(nd), . . . , (−rr+1)-th diagonals from the top down. If the0-th diagonal is along the line connecting the element a_(1,1) anda_(rr,rr), the diagonals parallel with the 0-th diagonal are the 1^(st),2^(nd), . . . , (rr−1)-th diagonals from the bottom up, and thediagonals parallel with the 0-th diagonal are the −1^(st), −2^(nd), . .. , (−rr+1)-th diagonals from the top down.

It is to be noted that, for a matrix M as an example, if M is not asquare matrix, the number, rr, of its rows can be larger than thenumber, cc, of its columns. For the matrix

$\quad\begin{pmatrix}a_{1,1} & a_{1,2} & \ldots & a_{1,{cc}} \\a_{2,1} & a_{2,2} & \ldots & a_{2,{cc}} \\\vdots & \vdots & \ddots & \vdots \\a_{{rr},1} & a_{{rr},2} & \ldots & a_{{rr},{cc}}\end{pmatrix}$

as an example, if the 0-th diagonal is along the line connecting theelement a_(rr,1) and a_(rr-cc+1,cc), the diagonals parallel with the0-th diagonal are the 1^(st), 2^(nd), . . . , (rr−1)-th diagonals fromthe bottom up, and the diagonals parallel with the 0-th diagonal are the(−1)^(st), (−2)^(nd), . . . , (−rr+1)-th diagonals from the top down. Ifthe 0-th diagonal is along the line connecting the element a_(rr-cc+1,1)and a_(rr,cc), the diagonals parallel with the 0-th diagonal are the1^(st)2^(nd), . . . , (rr−1)-th diagonals from the bottom up, and thediagonals parallel with the 0-th diagonal are the −1^(st), −2^(nd), . .. , (−rr+1)-th diagonals from the top down.

It is to be noted that, when the predetermined number of indices areselected from M_(re) row by row, column by column or diagonal bydiagonal, each index corresponding to a non-transmitted bit sequence ina second bit sequence matrix is skipped. The second bit sequence matrixis obtained from a first bit sequence matrix by using a secondpredetermined transform. The first bit sequence matrix is formed fromthe Polar encoded bit sequence. The second predetermined transformincludes row permutation or column permutation.

It is to be noted that, if the encoded bit sequence is {x₀, x₁, x₂, . .. , x₁₅} and the bit sequence to be transmitted is {x₆, x₇, . . . ,x₁₅)}, then the indices corresponding to the non-transmitted bitsequence are {0, 1, 2, . . . , 5}. In this case, when the indices inM_index are selected based on M_(re), the indices {0, 1, 2, . . . , 5}are to be skipped.

It is to be noted that the operation of selecting T bits based on thesecond bit sequence matrix as the bit sequence to be transmittedincludes: selecting T bits based on the second bit sequence matrix rowby row, column by column or diagonal by diagonal, as the bit sequence tobe transmitted.

It is to be noted that the operation of selecting T bits based on thesecond bit sequence matrix row by row, column by column or diagonal bydiagonal as the bit sequence to be transmitted includes: selecting Tbits based on the second bit sequence matrix row by row, column bycolumn or diagonal by diagonal, from a starting position t in the secondbit sequence matrix. When the selection reaches the first or last bit inthe second bit sequence matrix, it continues with the last or first bitin the second bit sequence matrix, where 1≤t≤R_(vb)×C_(vb).

It is to be noted that the operation of selecting T bits based on thesecond bit sequence matrix row by row, column by column or diagonal bydiagonal as the bit sequence to be transmitted includes: selecting the1^(st) to T-th bits or the (N−T+1)-th to N-th bits from the second bitsequence matrix column by column, when T is smaller than or equal to alength N of the Polar encoded bit sequence; selecting the 1^(st) to T-thbits or the (N−T+1)-th to N-th bits from the second bit sequence matrixrow by row, when T is smaller than or equal to the length N of the Polarencoded bit sequence; selecting the 1^(st) to T-th bits or the(N−T+1)-th to N-th bits from the second bit sequence matrix diagonal bydiagonal, when T is smaller than or equal to the length N of the Polarencoded bit sequence; selecting, when T is larger than the length N ofthe Polar encoded bit sequence, T bits row by row, column by column ordiagonal by diagonal, from the t-th bit in the second bit sequencematrix. When the selection reaches the first or last bit in the secondbit sequence matrix, it continues with the last or first bit in thesecond bit sequence matrix, where 1≤t≤R_(vb)×C_(vb) and N is anon-negative integer.

It is to be noted that the operation of selecting T bits from the secondbit sequence matrix column by column includes at least one of: selectingT_(ie1) bits from the 1^(st), 2^(nd), . . . , E₁-th columns, whereΣ_(ie1=1) ^(E) ¹ T_(ie1)=T, 1≤E₁≤C_(vb), and ie1 and E₁ are integers;selecting T_(ie2) bits from the E₂-th, (E₂+1)-th, . . . , E₃-th columns,where Σ_(ie2=E) ₂ ^(E) ³ T_(ie2)=T, 1≤E₂≤E₃≤C_(re), and ie2, E₂ and E₃are integers; or selecting T_(ie3) bits from the E₄-th, (E₄+1)-th, . . ., E_(vb)-th columns, where Σ_(ie3=E) ₄ ^(C) ^(vb) T_(ie3)=T,1≤E₄≤C_(vb), and ie3 and E₄ are integers.

It is to be noted that the operation of selecting T bits from the secondbit sequence matrix row by row includes at least one of: selecting Tinbits from the 1^(st), 2^(nd), . . . , F₁-th rows, where Σ_(if1=1) ^(F) ¹T_(if1)=T, 1≤F≤R_(vb), and if1 and F₁ are integers; selecting T_(if2)bits from the F₂-th, (F₂+1)-th, . . . , F₃-th rows, where Σ_(if2=F) ₂^(F) ³ T_(if2)=T, 1≤F₂≤F₃≤R_(vb), and if2, F₂ and F₃ are integers; orselecting T_(if3) bits from the F₄-th, (F₄+1)-th, . . . , R_(vb)-throws, where Σ_(if3=F) ₄ ^(R) ^(vb) T_(if3)=T, 1≤F₄≤R_(vb), and if3 andF₄ are integers.

It is to be noted that the operation of selecting T bits from the secondbit sequence matrix diagonal by diagonal includes at least one of:selecting T_(ig1) bits from the (−min(R_(vb), C_(vb))+1)-th,(−min(R_(vb), C_(vb))+2)-th, . . . , G₁-th diagonals, whereΣ_(ig1=−min(R) _(vb) _(, C) _(vb) ₎₊₁ ^(G) ¹ T_(ig1)=T, −min(R_(vb),C_(vb))+≤G₁≤max(R_(vb), C_(vb))−1, and ig1 and G₁ are integers;selecting K_(ig2) bits from the G₂-th, (G₂+1)-th, . . . , G₃-thdiagonals, where Σ_(ig2=G) ₂ ^(G) ³ T_(ig2)=T, −min(R_(vb),C_(vb))+1≤G₂≤G₃≤max(R_(vb), C_(vb))−1, and ig2, G₂ and G₃ are integers;or selecting K_(id3) bits from the G₄-th, (G₄+1)-th, . . . ,(max(R_(vb), C_(vb))−1)-th diagonals, where

${{{\sum_{{{ig}\; 3} = G_{4}}^{{\max {({R_{vb},C_{vb}})}} - 1}T_{{ig}\; 3}} = T},}\;$

−min(R_(vb), C_(vb))+1≤G₄≤max(R_(vb), C_(vb))−1, and ig3 and G₄ areintegers.

In an example, the bit sequence in M_(vb) can be arranged as

$M_{vb} = {\begin{bmatrix}y_{0} & y_{1} & y_{2} & y_{3} \\y_{4} & y_{5} & y_{6} & y_{7} \\y_{8} & y_{9} & y_{10} & y_{11} \\y_{12} & y_{13} & y_{14} & y_{15}\end{bmatrix}.}$

Let T=9, when the first 9 bits are selected row by row to form the bitsequence to be transmitted, {y₀, y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈} areselected to form the bit sequence to be transmitted. When the first 9bits are selected column by column to form the bit sequence to betransmitted, {y₀, y₄, y₈, y₁₂, y₁, y₅, y₉, y₁₃, y₂} are selected to formthe bit sequence to be transmitted. When the first 9 bits are selecteddiagonal by diagonal to form the bit sequence to be transmitted, {y₀,y₁, y₄, y₂, y₅, y₈, y₃, y₆, y₉} are selected to form the bit sequence tobe transmitted. When the last 9 bits are selected row by row to form thebit sequence to be transmitted, {y₇, y₈, y₉, y₁₀, y₁₁, y₁₂, y₁₃, y₁₄,y₁₅} are selected to form the bit sequence to be transmitted. When thelast 9 bits are selected column by column to form the bit sequence to betransmitted, {y₁₃, y₂, y₆, y₁₀, y₁₄, y₃, y₇, y₁₁, y₁₅} are selected toform the bit sequence to be transmitted. When the last 9 bits areselected diagonal by diagonal to form the bit sequence to betransmitted, {y₆, y₉, y₁₂, y₇, y₁₀, y₁₃, y₁₁, y₁₄, y₁₅} are selected toform the bit sequence to be transmitted. During the selection in order,when the selection reaches the last bit y₁₅ in M_(vb), it continues withthe first bit y₀ in M_(vb). During the selection in reverse order, whenthe selection reaches the first bit y₀ in M_(vb), it continues with thelast bit y₁₅ in M_(vb).

It is to be noted that the above steps can be, but not limited to be,performed by a base station or a terminal.

With the description of the above embodiments, it will be apparent tothose skilled in the art that the method according to the aboveembodiments can be implemented by means of software plus a necessarygeneral-purpose hardware platform. Of course it can be implemented inhardware, but in many cases the former is the optimal implementation.Based on this understanding, the technical solution of the presentdisclosure in essence, or parts thereof contributive to the prior art,can be embodied in the form of a software product. The computer softwareproduct can be stored in a storage medium (e.g., ROM/RAM, magnetic disk,or optical disc) and includes instructions for causing a terminal device(which may be a mobile phone, a computer, a server, or a network device,etc.) to perform the method described in the various embodiments of thepresent disclosure.

Embodiment 2

According to an embodiment of the present disclosure, an apparatus forsequence determination is also provided. The apparatus can be applied ina first station for implementing the above embodiments and examples(details thereof will be omitted here). As used hereinafter, the term“module” can be software, hardware, or a combination thereof, capable ofperforming a predetermined function. While the apparatuses to bedescribed in the following embodiments can be implemented in software,it can be contemplated that they can also be implemented in hardware ora combination of software and hardware.

FIG. 3 is a block diagram showing a structure of an apparatus forsequence determination according to an embodiment of the presentdisclosure. As shown in FIG. 3, the apparatus includes:

a permuting module 32 configured to map a first bit sequence having alength of K bits to a specified position based on M_index to obtain asecond bit sequence;

an encoding module 34 coupled to the above permuting module 32 andconfigured to apply Polar encoding to the second bit sequence to obtaina Polar encoded bit sequence; and

a selecting module 36 coupled to the above encoding module 34 andconfigured to select T bits based on the Polar encoded bit sequence as abit sequence to be transmitted, where K and T are both non-negativeintegers and K≤T.

With the above apparatus, a first bit sequence having a length of K bitsis mapped to a specified position based on M_index to obtain a secondbit sequence. Polar encoding is applied to the second bit sequence toobtain a Polar encoded bit sequence. T bits are selected based on thePolar encoded bit sequence as a bit sequence to be transmitted. That is,the present disclosure provides a method for determining a bit sequenceto be transmitted, capable of solving the problem in the related artassociated with lack of a sequence determination scheme in the 5G NewRAT.

In an embodiment of the present disclosure, the above apparatus mayfurther include: a first transform module coupled to the above permutingmodule 32 and configured to apply a first predetermined transform to afirst index matrix to obtain a second index matrix and obtain M_indexbased on the second index matrix. The first predetermined transformincludes row permutation or column permutation. That is, in the Polarencoding process, the same transform pattern is applied to one dimensionof the first index matrix, such that only the other dimension of thefirst index matrix needs to be changed when a mother code lengthchanges. Thus, the hardware can be reused in the implementation of Polarcodes, thereby solving the problem in the related art associated withincapability of hardware reuse in the Polar encoding process.

In an embodiment of the present disclosure, the apparatus may furtherinclude: a second transform module configured to form a first bitsequence matrix from the Polar encoded bit sequence, and apply a secondpredetermined transform to the first bit sequence matrix to obtain asecond bit sequence matrix. The second predetermined transform includesrow permutation or column permutation. The selecting module is furtherconfigured to select T bits based on the second bit sequence matrix asthe bit sequence to be transmitted. That is, the same transform patternis applied to one dimension of the first index matrix, such that onlythe other dimension of the first index matrix needs to be changed when amother code length changes. Thus, the hardware can be further reused inthe implementation of Polar codes, thereby further solving the problemin the related art associated with incapability of hardware reuse in thePolar encoding process.

It is to be noted that the above apparatus may further include a storagemodule coupled to the above first transform module and configured tostore the second bit sequence matrix.

It is to be noted that the above storage module can be, but not limitedto, a buffer or any other memory, such as an internal memory or anyother logic entity.

It is to be noted that the above first index matrix can be, but notlimited to, a two dimensional, three dimensional or multi-dimensionalmatrix. In an example where the above first index matrix is a twodimensional matrix, the above first predetermined transform can beembodied such that a row transform pattern or a column transform patternfor the first index matrix is the same.

In an example where the above first index matrix is a two dimensionalmatrix, in an embodiment of the present disclosure, the second indexmatrix is M_(re), which is a matrix of R_(re) rows and C_(re) columns.The first index matrix is M_(or), which is:

$M_{or} = {\begin{bmatrix}0 & 1 & 2 & \ldots & {C_{re} - 1} \\C_{re} & {C_{re} + 1} & {C_{re} + 2} & \ldots & {{2C_{re}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{\left( {R_{re} - 1} \right) \times C_{re}} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 1} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 2} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}\mspace{14mu} {or}}$ ${M_{or} = \begin{bmatrix}0 & R_{re} & {2R_{re}} & \ldots & {\left( {C_{re} - 1} \right) \times R_{re}} \\1 & {R_{re} + 1} & {{2R_{re}} + 1} & \ldots & {{\left( {C_{re} - 1} \right) \times R_{re}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{R_{re} - 1} & {{2R_{re}} - 1} & {{3R_{re}} - 1} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}},$

where R_(re)×C_(re)≥N, R_(re) and C_(re) are both non-negative integers,and N is a length of the Polar encoded bit sequence.

It is to be noted that when R_(re) is constant, C_(re) is a minimumvalue satisfying R_(re)×C_(re)≥N; or when C_(re) is constant, R_(re) isa minimum value satisfying R_(re)×C_(re)≥N.

It is to be noted that the above first transform module is furtherconfigured to obtain the second index matrix according to at least oneof: the i-th column of M_(re) being obtained from the π₁(i)-th column ofM_(or) by means of column permutation, where 0≤i≤C_(re)−1,0≤π₁(i)≤C_(re)−1, R_(re)×C_(re)≥N, and i and π₁(i) are both non-negativeintegers; or the j-th row of M_(re) being obtained from the π₂(j)-th rowof M_(or), where 0≤j≤R_(re)−1, 0≤π₂(j)≤R_(re)−1, R_(re)×C_(re)≥N, and jand π₂(j) are both non-negative integers.

It is to be noted that the above π₁(i) can be obtained according to atleast one of:

Scheme 1: π₁(i)=BRO(i), where BRO( ) denotes a bit reverse orderingoperation which includes: converting a decimal number i into a firstbinary number (B_(n1-1), B_(n1-2), . . . , B₀), reversing the firstbinary number to obtain a second binary number (B₀, B₁, . . . ,B_(n1-1)) and converting the second binary number into a decimal numberπ₁(i), where n1=log₂(C_(re)) and 0≤i≤C_(re)−1;

Scheme 2: π₁(i)={S1, S2, S3}, where S1={0, 1, . . . , i1−1}, S2={i2, i3,i2+1, i3+1, . . . , i4, i5}, and S3 is a set of elements in {0, 1, . . ., C_(re)−1} other than those included in S1 and S2, whereC_(re)/8≤i1≤i2≤C_(re)/3, i2≤i4≤i3≤2C_(re)/3, i3≤i5≤C_(re)−1, i1, i2, i3,i4 and i5 are all non- negative integers, and an intersection of any twoof S1, S2 and S3 is null; or

Scheme 3: π₁(i)={I}, where {I} is a sequence obtained by organizingnumerical results of applying a function f(r) to column indices r ofM_(or) in ascending or descending order, where 0≤r≤C_(re)−1.

The above three schemes will be explained with reference to thefollowing examples.

For Scheme 1, if C_(re)=8, i=6, then n1=log₂(8)=3. i=6 is converted intoa binary number (B₂, B₁, B₀)=(1, 1, 0). The binary number (B₂, B₁,B₀)=(1, 1, 0) is reversed to obtain (B₀, B 1, B₂)=(0, 1, 1). (B₀, B₁,B₂)=(0, 1, 1) is then converted into a decimal number π₁(i)=3.

For Scheme 2, if C_(re)=8, i₁=2, i₂=2, i₃=4, i₄=3 and i₅=5, then S1={0,1}, S2={2, 4, 3, 5}, S3={6, 7}, and π₁(i)={0, 1, 2, 4, 3, 5, 6, 7}.

For Scheme 3, C_(re)=8, {f(0), . . . , f(7)}={0, 1, 1.18, 2.18, 1.41,2.41, 2.60, 3.60}. f(0), . . . , f(7) is organized in ascending order toobtain π₁(i)={1, 2, 3, 5, 4, 6, 7, 8}.

It is to be noted that f(r) includes at least one of:

${{f(r)} = {\sum_{{m\; 1} = 0}^{{n\; 1} - 1}{B_{m\; 1} \times 2^{\frac{m\; 1}{k}}}}},$

(B_(n1-1), B_(n1-2), . . . , B₀) is a binary representation of the indexr, where 0≤m1≤n1−1, n1=log₂(C_(re)), and k is a non-negative integer(e.g., C_(re)=8, i=6, k=4, n1=log₂(8)=3, i=6 is converted into a binarynumber (B₂, B₁, B₀)=(1, 1, 0),

$\left. {{f(6)} = {{\sum_{{m\; 1} = 0}^{{n\; 1} - 1}{B_{m\; 1} \times 2^{\frac{m\; 1}{4}}}} = {{{0 \times 2^{\frac{0}{4}}} + {1 \times 2^{\frac{1}{4}}} + {1 \times 2^{\frac{2}{4}}}} = 2.4142}}} \right);$

initializing a function value corresponding to r as f₁ ^((r)), andobtaining a function value for each element f_(C) _(re) ^((r)) aftern1-th iteration in accordance with a first iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 2}^{({{2r} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 2}^{(r_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 2}^{(r_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 2}^{({2r})} = {f_{m\; 2}^{(r_{1})} + f_{m\; 2}^{(r_{2})}}}\end{matrix},} \right.$

where f₁ ^((r)) is a mean log likelihood ratio (e.g., ≤(z) can beapproximately:

${\phi (z)} = \left\{ {\begin{matrix}{1 - {\frac{1}{\sqrt{4{\pi z}}}{\int_{- \infty}^{+ \infty}{\tanh \frac{u}{2}{\exp \left( {{- \left( {u - z} \right)^{2}}/\left( {4z} \right)} \right)}{du}}}}} & {z > 0} \\{1,{z = 0}} & \;\end{matrix},} \right.$

where the nodes i₁ and i₂ participating in the iterative calculation aredependent on the structure of the Polar encoder);

(Let the initial value f₁ ^((r))=2/σ², where σ² is the variance ofnoise, C_(re)=8, σ²=0. f₁ ^((r)) is substituted into the iterationequation to obtain f₂ ^((r)), which is then substituted into theiteration equation to obtain f₄ ^((r)), and so on, until f₈ ^((r)) iscalculated, where f(r)=f₈ ^((r)), 0≤r≤C_(re)−1, {f(0), . . . ,f(7)}={0.04, 0.41, 0.61, 3.29, 1.00, 4.56, 5.78, 16.00}); or

initializing a function value corresponding to r as f₁ ^((r)), andobtaining a function value for each element f_(C) _(re) ^((r)) aftern1-th iteration in accordance with a second iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 3}^{({{2r} - 1})} = {f_{m\; 3}^{(r_{1})} + f_{m\; 3}^{(r_{2})} - {f_{m\; 3}^{(r_{1})}f_{m\; 3}^{(r_{2})}}}} \\{f_{2m\; 3}^{({2r})} = {f_{m\; 3}^{(r_{1})}f_{m\; 3}^{(r_{2})}}}\end{matrix},} \right.$

where f₁ ^((r)) is mutual information, where 1≤m2≤n1, 1≤m3≤n1, and r1,r2, 2r and 2r−1 are all integers larger than or equal to 0 and smallerthan or equal to C_(re)−1 (the nodes i₁ and i₂ participating in theiterative calculation are dependent on the structure of the Polarencoder);

(Let f₁ ^((r))=0.5 and C_(re)=8. f₁ ^((r)) is substituted into theiteration equation to obtain f₂ ^((r)), which is then substituted intothe iteration equation to obtain f₄ ^((r)), and so on, until f₈ ^((r))is calculated, where f(r)=f₈ ^((r)), 0≤i≤C_(re)−1, {f(0), . . . ,f(7)}={0.008, 0.152, 0.221, 0.682, 0.313, 0.779, 0.850, 0.991}).

It is to be noted that the above π₂(j) can be obtained according to atleast one of:

π₂(j)=BRO(j), where BRO( ) denotes a bit reverse ordering operationwhich includes: converting a decimal number j into a third binary number(B_(n2-1), B_(n2-2), . . . , B₀), reversing the third binary number toobtain a fourth binary number (B₀, B₁, . . . , B_(n2-1)) and convertingthe fourth binary number into a decimal number π₂(j), wheren2=log₂(R_(re)) and 0≤j≤R_(re)−1;

π₂(j)={S4, S5, S6}, where S4={0, 1, . . . , j1−1}, S5={j2, j3, j2+1,j3+1, . . . , j4, j5}, and S6 is a set of elements in {0, 1, . . . ,R_(re)−1} other than those included in S4 and S5, whereR_(re)/8≤j1≤j2≤R_(re)/3, j2≤j4≤j3≤2 R_(re)/3, j3≤j5≤R_(re)−1, j1, j2,j3, j4 and j5 are all non- negative integers, and an intersection of anytwo of S4, S5 and S6 is null; or

π₂(j)={J}, where {J} is a sequence obtained by organizing numericalresults of applying a function f(s) to row indices s of M_(or) inascending or descending order, where 0≤s≤R_(re)−1.

It is to be noted that f(s) includes at least one of:

${{f(s)} = {\sum_{{m\; 4} = 0}^{{n\; 2} - 1}{B_{m\; 4} \times 2^{\frac{m\; 4}{k}}}}},$

(B_(n2-1), B_(n2-2), . . . , B₀) is a binary representation of the indexs, where 0≤m4≤n2−1, n2=log₂(R_(re)), and k is a non-negative integer;

initializing a function value corresponding to s as f₁ ^((s)), andobtaining a function value for each element f_(R) _(re) ^((s)) e aftern2-th iteration in accordance with a third iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 5}^{({{2s} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 5}^{(s_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 5}^{(s_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 5}^{({2s})} = {f_{m\; 5}^{(s_{1})} + f_{m\; 5}^{(s_{2})}}}\end{matrix},} \right.$

where f₁ ^((s)) is a mean log likelihood ratio; or

initializing a function value corresponding to s as f₁ ^((s)), andobtaining a function value for each element f_(R) _(re) ^((s)) aftern2-th iteration in accordance with a fourth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 6}^{({{2s} - 1})} = {f_{m\; 6}^{(s_{1})} + f_{m\; 6}^{(s_{2})} - {f_{m\; 6}^{(s_{1})}f_{m\; 6}^{(s_{2})}}}} \\{f_{2m\; 6}^{({2s})} = {f_{m\; 6}^{(s_{1})}f_{m\; 6}^{(s_{2})}}}\end{matrix},} \right.$

where f₁ ^((s)) is mutual information, where 1≤m5≤n2, 1≤m6≤n2, s1, s2,2s and 2s−1 are all integers larger than or equal to 0 and smaller thanor equal to R_(re)−1.

It is to be noted that, for explanations for the above π₂(j), referencecan be made to π₁(i).

It is to be noted that the above first bit sequence matrix can be, butnot limited to, a two dimensional, three dimensional ormulti-dimensional matrix. In an example where the above first bitsequence matrix is a two dimensional matrix, the above secondpredetermined transform can be embodied such that a row transformpattern or a column transform pattern for the first bit sequence matrixis the same.

It is to be noted that the first bit sequence matrix is M_(og). Thesecond bit sequence matrix is M_(vb), which is a matrix of R_(vb) rowsand C_(vb) columns. M_(og) is:

$M_{og} = {\begin{bmatrix}x_{0} & x_{1} & x_{2} & \ldots & x_{C_{vb} - 1} \\x_{C_{vb}} & x_{C_{vb} + 1} & x_{C_{vb} + 2} & \ldots & x_{{2C_{vb}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{{({R_{vb} - 1})} \times C_{vb}} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 1} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 2} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}\mspace{14mu} {or}}$$\mspace{20mu} {{M_{og} = \begin{bmatrix}x_{0} & x_{R_{vb}} & x_{2R_{vb}} & \ldots & x_{{({C_{vb} - 1})} \times R_{vb}} \\x_{1} & x_{R_{vb} + 1} & x_{{2R_{vb}} + 1} & \ldots & x_{{{({C_{vb} - 1})} \times R_{vb}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{R_{vb} - 1} & x_{{2R_{vb}} - 1} & x_{{3R_{vb}} - 1} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}},}$

where x₀, x₁, x₂, . . . , x_(R) _(vb) _(×C) _(vb) ₋₁ is the Polarencoded bit sequence, R_(vb)×C_(vb)≥N, R_(vb) and C_(vb) are bothnon-negative integers and N is a length of the Polar encoded bitsequence.

It is to be noted that when R_(vb) is constant, C_(vb) is a minimumvalue satisfying R_(vb)×C_(vb)≥N; or when C_(vb) is constant, R_(vb) isa minimum value satisfying R_(vb)×C_(vb)≥N.

It is to be noted that the above second transform module can further beconfigured to obtain the second bit sequence matrix according to atleast one of: the g-th column of M_(vb) being obtained from the π₃(g)-thcolumn of M_(og) by means of column permutation, where 0≤g≤C_(vb)−1,0≤π₃(g)≤C_(vb)−1, R_(vb)×C_(vb)≥N, and g and π₃(g) are both non-negativeintegers; or the h-th row of M_(vb) being obtained from the π₄(h)-th rowof M_(og) by means of row permutation, where 0≤h≤R_(vb)−1,0≤π₄(h)≤R_(vb)−1, R_(vb)×C_(vb)≥N, and h and π₄(h) are both non-negativeintegers.

It is to be noted that π₃(g) can be obtained according to at least oneof:

π₃(g)=BRO(g), where BRO( ) denotes a bit reverse ordering operationwhich includes: converting a decimal number g into a fifth binary number(B_(n3-1), B_(n3-2), . . . , B₀), reversing the fifth binary number toobtain a sixth binary number (B₀, B₁₁, . . . , B_(n3-1)) and convertingthe sixth binary number into a decimal number π₃(g), wheren3=log₂(C_(vb)) and 0≤g≤C_(vb)−1;

π₃(g)={S1, S2, S3}, where S1={0, 1, . . . , g1−1}, S2={g2, g3, g2+1,g3+1, . . . , g4, g5}, and S3 is a set of elements in {0, 1, . . . ,C_(vb)−1} other than those included in S1 and S2, whereC_(vb)/8≤g1≤g2≤C_(vb)/3, g2≤g4≤g3≤2C_(vb)/3, g3≤g5≤C_(vb)−1, g1, g2, g3,g4 and g5 are all non- negative integers, and an intersection of any twoof S1, S2 and S3 is null;

π₃(g)={G}, where {G} is a sequence obtained by organizing numericalresults of applying a function f(α) to column indices α of M_(og) inascending or descending order, where 0≤α≤C_(vb)−1;

π₃(g)={Q1, Q2, Q3}, where Q2={q1, q2, q1+1, q2+1, . . . , q3, q4},0≤q1≤q3≤(C_(vb)−1)/2, 0≤q2≤q4≤(C_(vb)−1)/2, q1, q2, q3, q4 and q5 areall non-negative integers, Q1 and Q3 are other elements in a differenceset between {0, 1, . . . , C_(vb)−1} and Q2, and an intersection of anytwo of Q1, Q2 and Q3 is null;

π₃(g) being different from a predefined sequence V1 in nV1 positions,where V1=={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 13, 17, 14, 18,15, 19, 20, 24, 21, 22, 25, 26, 28, 23, 27, 29, 30, 31}, 0≤nV1≤23; or

π₃(g) being different from a predefined sequence V2 in nV2 positions,where V2={0, 1, 2, 4, 3, 5, 6, 7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20,13, 21, 14, 22, 15, 23, 24, 25, 26, 28, 27, 29, 30, 31}, 0≤nV2≤3.

It is to be noted that f(α) includes at least one of:

${{f(\alpha)} = {\sum_{{m\; 6} = 0}^{{n\; 3} - 1}{B_{m\; 6} \times 2^{\frac{m\; 6}{k}}}}},$

(B_(n3-1), B_(n3-2), . . . , B₀) is a binary representation of the indexα, where 0≤m6≤n3−1, n3=log₂(C_(vb)), and k is a non-negative integer;

initializing a function value corresponding to α as f₁ ^((α)), andobtaining a function value for each element f_(C) _(vb) ^((α)) aftern3-th iteration in accordance with a fifth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 7}^{({{2\alpha} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 7}^{(\alpha_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 7}^{(\alpha_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 7}^{({2\alpha})} = {f_{m\; 7}^{(\alpha_{1})} + f_{m\; 7}^{(\alpha_{2})}}}\end{matrix},} \right.$

where f₁ ^((α)) is a mean log likelihood ratio; or

initializing a function value corresponding to s as f₁ ^((α)), andobtaining a function value for each element f_(C) _(vb) ^((α)) aftern3-th iteration in accordance with a sixth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 8}^{({{2\alpha} - 1})} = {f_{m\; 8}^{(\alpha_{1})} + f_{m\; 8}^{(\alpha_{2})} - {f_{m\; 8}^{(\alpha_{1})}f_{m\; 8}^{(\alpha_{2})}}}} \\{f_{2m\; 8}^{({2\alpha})} = {f_{m\; 8}^{(\alpha_{1})}f_{m\; 8}^{(\alpha_{2})}}}\end{matrix},} \right.$

where f₁ ^((α)) is mutual information, where 1≤m7≤n3, 1≤m8≤n3, and α1,α2, 2α and 2α−1 are all integers larger than or equal to 0 and smallerthan or equal to C_(vb)−1.

It is to be noted that π₄(h) can be obtained according to at least oneof:

π₄(h)=BRO(h), where BRO( ) denotes a bit reverse ordering operationwhich includes: converting a decimal number h into a seventh binarynumber (B_(n4-1), B_(n4-2), . . . , B₀), reversing the seventh binarynumber to obtain an eighth binary number (B₀, B₁, . . . , B_(n4-1)) andconverting the eighth binary number into a decimal number π₄(h), wheren4=log₂(R_(vb)) and 0≤h≤R_(vb)−1;

π₄(h)={S4, S5, S6}, where S4={0, 1, . . . , h1−1}, S5={h2, h3, h2+1,h3+1, . . . , h4, h5}, and S6 is a set of elements in {0, 1, . . . ,R_(vb)−1} other than those included in S4 and S5, whereR_(vb)/8≤h1≤h2≤R_(vb)/3, h2≤h4≤h3≤2R_(vb)/3, h3≤h5≤R_(vb)−1, h1, h2, h3,h4 and h5 are all non- negative integers, and an intersection of any twoof S4, S5 and S6 is null;

π₄(h)={H}, where {H} is a sequence obtained by organizing numericalresults of applying a function f(β) to row indices β of M_(og) inascending or descending order, where 0≤O3≤R_(vb)−1;

π₄(h)={O1, O2, O3}, where O2={o1, o2, o1+1, o2+1, . . . , o3, o4},0≤o1≤o3≤(R_(vb)−1)/2, 0≤o2≤o4≤(R_(vb)−1)/2, o1, o2, o3, o4 and o5 areall non-negative integers, O1 and O3 are other elements in a differenceset between {0, 1, . . . , R_(vb)−1} and O2, and an intersection of anytwo of O1, O2 and O3 is null;

π₄(h) being different from a predefined sequence VV1 in nVV1 positions,where VV1={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 13, 17, 14, 18,15, 19, 20, 24, 21, 22, 25, 26, 28, 23, 27, 29, 30, 31}, 0≤nVV1≤23; or

π₄(h) being different from a predefined sequence VV2 in nVV2 positions,where VV2={0, 1, 2, 4, 3, 5, 6, 7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20,13, 21, 14, 22, 15, 23, 24, 25, 26, 28, 27, 29, 30, 31}, 0≤nVV2≤3.

It is to be noted that f(β) includes at least one of:

${{f(\beta)} = {\sum_{{m\; 9} = 0}^{{n\; 4} - 1}{B_{m\; 9} \times 2^{\frac{m\; 9}{k}}}}},$

(B_(n4-1), B_(n4-2), . . . , B₀) is a binary representation of the indexβ, where 0≤m9≤n4−1, n4=log₂(R_(vb)), and k is a non-negative integer;

initializing a function value corresponding to β as f₁ ^((β)), andobtaining a function value for each element f_(R) _(vb) ^((β)) aftern4-th iteration in accordance with a seventh iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 10}^{({{2\beta} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 10}^{(\beta_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 10}^{(\beta_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 10}^{({2\beta})} = {f_{m\; 10}^{(\beta_{1})} + f_{m\; 10}^{(\beta_{2})}}}\end{matrix},} \right.$

where f₁ ^((β)) is a mean log likelihood ratio; or

initializing a function value corresponding to β as f₁ ^((β)), andobtaining a function value for each element f_(R) _(vb) ^((β)) aftern4-th iteration in accordance with an eighth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 11}^{({{2\beta} - 1})} = {f_{m\; 11}^{(\beta_{1})} + f_{m\; 11}^{(\beta_{2})} - {f_{m\; 11}^{(\beta_{1})}f_{m\; 11}^{(\beta_{2})}}}} \\{f_{2m\; 11}^{({2\beta})} = {f_{m\; 11}^{(\beta_{1})}f_{m\; 11}^{(\beta_{2})}}}\end{matrix},} \right.$

where f₁ ^((β)) is mutual information, where 1≤m10≤n4, 1≤m11≤n4, and β1,β2, 2β and 2β−1 are all integers larger than or equal to 0 and smallerthan or equal to R_(vb)−1.

It is to be noted that, for explanations for π₃(g) and π₄(h), referencecan be made to π₁(i) and descriptions thereof will be omitted here.

In an embodiment of the present disclosure, the above first transformmodule can further be configured to select a predetermined number ofindices based on M_(re) row by row, column by column or diagonal bydiagonal, as M_index.

It is to be noted that the operation of selecting the predeterminednumber of indices from M_(re) column by column includes: selecting π_(p)indices from the p-th column of M_(re), where Σ_(p=1) ^(C) ^(re)K_(p)=K, p is an integer, and 1≤p≤C_(re). The operation of selecting thepredetermined number of indices from M_(re) row by row includes:selecting π_(q) indices from the q-th row of M_(re), where Σ_(q=1) ^(R)^(re) K_(q)=K, q is an integer, and 1≤q≤R_(re). The operation ofselecting the predetermined number of indices from M_(re) diagonal bydiagonal includes: selecting K_(δ) indices from the δ-th diagonal ofM_(re), where

${{{\sum_{\delta = {{- {\min {({R_{re},C_{re}})}}} + 1}}^{{\max {({R_{re},C_{re}})}} - 1}K_{\delta}} = K},}\;$

δ is an integer, and −min(R_(re), C_(re))+1≤δ≤max(R_(re), C_(re))−1,where min(R_(re), C_(re)) denotes the smaller of R_(re) and C_(re), andmax(R_(re), C_(re)) denotes the larger of R_(re) and C_(re).

It is to be noted that the operation of selecting the predeterminednumber of indices from M_(re) column by column includes at least one of:selecting K_(ic1) indices from the 1^(st), 2^(nd)C₁-th columns ofM_(re), where Σ_(ic1=1) ^(C) ¹ K_(ic1)=K, 1≤ic1≤C₁, 1≤C₁≤C_(re), and ic1and C₁ are integers; selecting K_(ic2) indices from the C₂-th,(C₂+1)-th, . . . , C₃-th columns of M_(re), where Σ_(ic2=C) ₂ ^(C) ³K_(ic2)=K, C₂≤ic2≤C₃, 1≤C₂≤C₃≤C_(re), and ic2, C₂ and C₃ are integers;or selecting K_(ic3) indices from the C₄-th, (C₄+1)-th, . . . ,C_(re)-th columns of M_(re), where Σ_(ic3=C) ₄ ^(C) ^(re) K_(ic3)=K,C₄≤ic3≤C_(re), 1≤C₄≤C_(re), and ic3 and C₄ are integers.

It is to be noted that the operation of selecting the predeterminednumber of indices from M_(re) row by row includes at least one of:selecting K_(ir1) indices from the 1^(st), 2^(nd), . . . , R₁-th rows ofM_(re), where Σ_(ir1=1) ^(R) ¹ K_(ir1)=K, 1≤ir1≤R₁, 1≤R₁≤R_(re), and ir1and R₁ are integers; selecting K_(ir2) indices from the R₂-th,(R₂+1)-th, . . . , R₃-th rows of M_(re), where Σ_(ir2=R) ₂ ^(R) ³K_(ir2)=K, R₂≤ir2≤R₃, 1≤R₂≤R₃≤R_(re), and ir2, R₂ and R₃ are integers;or selecting K_(ir3) indices from the R₄-th, (R₄+1)-th, . . . R_(re)-throws of M_(re), where Σ_(ir3=R) ₄ ^(R) ^(re) K_(p)=K, 1≤R₄R_(re), andir3 and R₄ are integers.

It is to be noted that the operation of selecting the predeterminednumber of indices from M_(re) diagonal by diagonal includes at least oneof: selecting K_(id1) indices from the (−min(R_(re), C_(re))+1)-th,(−min(R_(re), C_(re))+2)-th, . . . , D₁-th diagonals of M_(re), whereΣ_(id1=−min(R) _(re) _(, C) _(re) ₎₊₁ ^(D) ¹ K_(id1)=K, −min(R_(re),C_(re))+1≤D₁≤max(R_(re), C_(re))−1, and id1 and D₁ are integers;selecting K_(id2) indices from the D₂-th, (D₂+1)-th, . . . , D₃-thdiagonals of M_(re), where Σ_(id2=D) ₂₁ ^(D) ³ K_(id2)=K, −min(R_(re),C_(re))+1≤D₂≤D₃≤max(R_(re), C_(re))−1, and id2, D₂ and D₃ are integers;and selecting K_(id3) indices from the D₄-th, (D₄+1)-th, . . . ,(max(R_(re), C_(re))−1)-th diagonals of M_(re), where

${{{\sum_{{{id}\; 3} = D_{4}}^{{\max {({R_{re},C_{re}})}} - 1}K_{{id}\; 3}} = K},}\;$

−min(R_(re), C_(re))+1≤D₄≤max(R_(re), C_(re))−1, and id3 and D₄ areintegers, where min(R_(re), C_(re)) denotes the smaller of R_(re) andC_(re), and max(R_(re), C_(re)) denotes the larger of R_(re) and C_(re).

It is to be noted that, when the predetermined number of indices areselected from M_(re) row by row, column by column or diagonal bydiagonal, each index corresponding to a non-transmitted bit sequence ina second bit sequence matrix is skipped. The second bit sequence matrixis obtained from a first bit sequence matrix by using a secondpredetermined transform. The first bit sequence matrix is formed fromthe Polar encoded bit sequence. The second predetermined transformincludes row permutation or column permutation.

It is to be noted that the above selecting module 36 can further beconfigured to select T bits based on the second bit sequence matrix rowby row, column by column or diagonal by diagonal, as the bit sequence tobe transmitted.

It is to be noted that the above selecting module 36 can further beconfigured to select T bits from the second bit sequence matrix row byrow, column by column or diagonal by diagonal, from a starting positiont in the second bit sequence matrix. When the selection reaches thefirst or last bit in the second bit sequence matrix, it continues withthe last or first bit in the second bit sequence matrix, where1≤t≤R_(vb)×C_(vb).

It is to be noted that the above selecting module 36 can further beconfigured to select the 1^(st) to T-th bits or the (N−T+1)-th to N-thbits from the second bit sequence matrix column by column, when T issmaller than or equal to a length N of the Polar encoded bit sequence;select the 1^(st) to T-th bits or the (N−T+1)-th to N-th bits from thesecond bit sequence matrix row by row, when T is smaller than or equalto the length N of the Polar encoded bit sequence; select the 1^(st) toT-th bits or the (N−T+1)-th to N-th bits from the second bit sequencematrix diagonal by diagonal, when T is smaller than or equal to thelength N of the Polar encoded bit sequence; select, when T is largerthan the length N of the Polar encoded bit sequence, T bits row by row,column by column or diagonal by diagonal, from the t-th bit in thesecond bit sequence matrix. When the selection reaches the first or lastbit in the second bit sequence matrix, it continues with the last orfirst bit in the second bit sequence matrix, where 1≤t≤R_(vb)×C_(vb) andN is a non-negative integer.

It is to be noted that the operation of selecting T bits from the secondbit sequence matrix column by column includes at least one of: selectingT_(ie1) bits from the 1^(st), 2^(nd), . . . , E₁-th columns, whereΣ_(ie1=1) ^(E) ¹ T_(ie1)=T, 1≤E₁≤C_(vb), and ie1 and E₁ are integers;selecting T_(ie2) bits from the E₂-th, (E₂+1)-th, . . . , E₃-th columns,where Σ_(ie2=E) ₂ ^(E) ³ T_(ie2)=T, 1≤E₂≤E₃≤C_(re), and ie2, E₂ and E₃are integers; or selecting T_(ie3) bits from the E₄-th, (E₄+1)-th, . . ., E_(vb)-th columns, where Σ_(ie3=E) ₄ ^(C) ^(vb) T_(ie3)=T,1≤E₄≤C_(vb), and ie3 and E₄ are integers.

It is to be noted that the operation of selecting T bits from the secondbit sequence matrix row by row includes at least one of: selecting Tinbits from the 1^(st), 2^(nd), . . . , F₁-th rows, where Σ_(if1=1) ^(F) ¹T_(if1)=T, 1≤F₁≤R_(vb), and if1 and F₁ are integers; selecting T_(if2)bits from the F₂-th, (F₂+1)-th, . . . , F₃-th rows, where Σ_(if2=F) ₂^(F) ³ T_(if2)=T, 1≤F₂F₃≤R_(vb), and if2, F₂ and F₃ are integers; orselecting T_(ir3) bits from the F₄-th, (F₄+1)-th, . . . , R_(vb)-throws, where Σ_(if3=F) ₄ ^(R) ^(vb) T_(if3)=T, 1≤F₄≤R_(vb), and if3 andF₄ are integers.

It is to be noted that the operation of selecting T bits from the secondbit sequence matrix diagonal by diagonal includes at least one of:selecting T_(ig1) bits from the (−min(R_(vb), C_(vb))+1)-th,(−min(R_(vb), C_(vb))+2)-th, . . . , G₁-th diagonals, whereΣ_(ig1=−min(R) _(vb) _(, C) _(vb) ₎₊₁ ^(G) ¹ T_(ig1)=T, −min(R_(vb),C_(vb))+≤G₁≤max(R_(vb), C_(vb))−1, and ig1 and G₁ are integers;selecting K_(ig2) bits from the G₂-th, (G₂+1)-th, . . . , G₃-thdiagonals, where Σ_(ig2=G) ₂ ^(G) ³ T_(ig2)=T, −min(R_(vb),C_(vb))+1≤G₂≤G₃≤max(R_(vb), C_(vb))−1, and ig2, G₂ and G₃ are integers;or selecting K_(id3) bits from the G₄-th, (G₄+1)-th, . . . ,(max(R_(vb), C_(vb))−1)-th diagonals, where

${{{\sum_{{{ig}\; 3} = G_{4}}^{{\max {({R_{vb},C_{vb}})}} - 1}T_{{ig}\; 3}} = T},}\;$

−min(R_(vb), C_(vb))+1≤G₄≤max(R_(vb), C_(vb))−1, and ig3 and G₄ areintegers.

It is to be noted that the above apparatus can be, but not limited tobe, provided in a terminal or a network device such as a base station.

It should be noted that each of the above-described modules can beimplemented by means of software or hardware, and the latter can beimplemented in, but not limited to, the following manner: theabove-described modules can be located at the same processor, or can bedistributed over a plurality of processors in any combination.

Embodiment 3

Embodiment 3 of the present disclosure provides a device. FIG. 4 is ablock diagram showing a structure of a device according to Embodiment 3of the present disclosure. AS shown in FIG. 4, the device includes:

a processor 42 configured to: map a first bit sequence having a lengthof K bits to a specified position based on M_index to obtain a secondbit sequence; apply Polar encoding to the second bit sequence to obtaina Polar encoded bit sequence; and select T bits based on the Polarencoded bit sequence as a bit sequence to be transmitted, where K and Tare both non-negative integers and K≤T, and

a memory 44 coupled to the processor 42.

With the above device, a first bit sequence having a length of K bits ismapped to a specified position based on M_index to obtain a second bitsequence. Polar encoding is applied to the second bit sequence to obtaina Polar encoded bit sequence. T bits are selected based on the Polarencoded bit sequence as a bit sequence to be transmitted. That is, thepresent disclosure provides a method for determining a bit sequence tobe transmitted, capable of solving the problem in the related artassociated with lack of a sequence determination scheme in the 5G NewRAT.

In an embodiment of the present disclosure, the above processor 42 canfurther be configured to: apply a first predetermined transform to afirst index matrix to obtain a second index matrix; and obtain M_indexbased on the second index matrix. The first predetermined transformincludes row permutation or column permutation. That is, in the Polarencoding process, the same transform pattern is applied to one dimensionof the first index matrix, such that only the other dimension of thefirst index matrix needs to be changed when a mother code lengthchanges. Thus, the hardware can be reused in the implementation of Polarcodes, thereby solving the problem in the related art associated withincapability of hardware reuse in the Polar encoding process.

In an embodiment of the present disclosure, the above processor 42 canfurther be configured to: write the Polar encoded bit sequence into afirst bit sequence matrix; and apply a second predetermined transform tothe first bit sequence matrix to obtain a second bit sequence matrix.The second predetermined transform includes row permutation or columnpermutation. A selecting module is configured to select T bits based onthe second bit sequence matrix as the bit sequence to be transmitted.That is, the same transform pattern is applied to one dimension of thefirst index matrix, such that only the other dimension of the firstindex matrix needs to be changed when a mother code length changes.Thus, the hardware can be further reused in the implementation of Polarcodes, thereby further solving the problem in the related art associatedwith incapability of hardware reuse in the Polar encoding process.

It is to be noted that the above storage module can be configured tostore the above second bit sequence matrix. The above storage module canbe, but not limited to, a buffer or any other memory, such as aninternal memory or any other logic entity.

It is to be noted that the above first index matrix can be, but notlimited to, a two dimensional, three dimensional or multi-dimensionalmatrix. In an example where the above first index matrix is a twodimensional matrix, the above first predetermined transform can beembodied such that a row transform pattern or a column transform patternfor the first index matrix is the same.

In an example where the above first index matrix is a two dimensionalmatrix, in an embodiment of the present disclosure, the second indexmatrix is M_(re), which is a matrix of R_(re) rows and C_(re) columns.The first index matrix is M_(or), which is:

$M_{or} = {\begin{bmatrix}0 & 1 & 2 & \ldots & {C_{re} - 1} \\C_{re} & {C_{re} + 1} & {C_{re} + 2} & \ldots & {{2C_{re}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{\left( {R_{re} - 1} \right) \times C_{re}} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 1} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 2} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}\mspace{14mu} {or}}$ ${M_{or} = \begin{bmatrix}0 & R_{re} & {2R_{re}} & \ldots & {\left( {C_{re} - 1} \right) \times R_{re}} \\1 & {R_{re} + 1} & {{2R_{re}} + 1} & \ldots & {{\left( {C_{re} - 1} \right) \times R_{re}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{R_{re} - 1} & {{2R_{re}} - 1} & {{3R_{re}} - 1} & \ldots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}},$

where R_(re)×C_(re)≥N, R_(re) and C_(re) are both non-negative integers,and N is a length of the Polar encoded bit sequence.

It is to be noted that when R_(re) is constant, C_(re) is a minimumvalue satisfying R_(re)×C_(re)≥N; or when C_(re) is constant, R_(re) isa minimum value satisfying R_(re)×C_(re)≥N.

It is to be noted that the above processor 42 can further be configuredto obtain the second index matrix according to at least one of: the i-thcolumn of M_(re) being obtained from the π₁(i)-th column of M_(or) bymeans of column permutation, where 0≤i≤C_(re)−1, 0≤π₁(i)≤C_(re)−1,R_(re)×C_(re)≥N, and i and π₁(i) are both non-negative integers; or thej-th row of M_(re) being obtained from the π₂(j)-th row of M_(or), where0≤j≤R_(re)−1, 0≤π2(j)≤R_(re)−1, R_(re)×C_(re)≥N, and j and π₂(j) areboth non-negative integers.

It is to be noted that the above π₁(i) can be obtained according to atleast one of:

Scheme 1: π₁(i)=BRO(i), where BRO( ) denotes a bit reverse orderingoperation which includes: converting a decimal number i into a firstbinary number (B_(n1-1), B_(n1-2), . . . , B₀), reversing the firstbinary number to obtain a second binary number (B₀, B₁, . . . ,B_(n1-1)) and converting the second binary number into a decimal numberπ₁(i), where n1=log₂(C_(re)) and 0≤i≤C_(re)−1;

Scheme 2: π₁(i)={S1, S2, S3}, where S1={0, 1, . . . , i1−1}, S2={i2, i3,i2+1, i3+1, . . . , i4, i5}, and S3 is a set of elements in {0, 1, . . ., C_(re)−1} other than those included in S1 and S2, whereC_(re)/8≤i1≤i2≤C_(re)/3, i2≤i4≤i3≤2C_(re)/3, i3≤i5≤C_(re)−1, i1, i2, i3,i4 and i5 are all non- negative integers, and an intersection of any twoof S1, S2 and S3 is null; or

Scheme 3: π₁(i)={I}, where {I} is a sequence obtained by organizingnumerical results of applying a function f(r) to column indices r ofM_(or) in ascending or descending order, where 0≤r≤C_(re)−1.

The above three schemes will be explained with reference to thefollowing examples.

For Scheme 1, if C_(re)=8, i=6, then n1=log₂(8)=3. i=6 is converted intoa binary number (B₂, B₁, B₀)=(1, 1, 0). The binary number (B₂, B₁,B₀)=(1, 1, 0) is reversed to obtain (B₀, B₁, B₂)=(0, 1, 1). (B₀, B₁,B₂)=(0, 1, 1) is then converted into a decimal number π₁(i)=3.

For Scheme 2, if C_(re)=8, i₁=2, i₂=2, i₃=4, i₄=3 and i₅=5, then S1={0,1}, S2={2, 4, 3, 5}, S3={6, 7}, and π₁(i)={0, 1, 2, 4, 3, 5, 6, 7}.

For Scheme 3, C_(re)=8, {f(0), . . . , f(7)}={0, 1, 1.18, 2.18, 1.41,2.41, 2.60, 3.60}. f(0), . . . , f(7) is organized in ascending order toobtain 1 i(i)={1, 2, 3, 5, 4, 6, 7, 8}.

It is to be noted that f(r) includes at least one of:

${{f(r)} = {\sum_{{m\; 1} = 0}^{{n\; 1} - 1}{B_{m\; 1} \times 2^{\frac{m\; 1}{k}}}}},$

(B_(n1-1), B_(n1-2), . . . , B₀) is a binary representation of the indexr, where 0≤m1≤n1−1, n1=log₂(C_(re)), and k is a non-negative integer(e.g., C_(re)=8, i=6, k=4, n1=log₂(8)=3, i=6 is converted into a binarynumber (B₂, B₁, B₀)=(1, 1, 0),

$\left. {{f(6)} = {{\sum_{{m\; 1} = 0}^{{n\; 1} - 1}{B_{m\; 1} \times 2^{\frac{m\; 1}{4}}}} = {{{0 \times 2^{\frac{0}{4}}} + {1 \times 2^{\frac{1}{4}}} + {1 \times 2^{\frac{2}{4}}}} = 2.4142}}} \right);$

initializing a function value corresponding to r as f₁ ^((r)), andobtaining a function value for each element f_(C) _(re) ^((r)) aftern1-th iteration in accordance with a first iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 2}^{({{2r} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 2}^{(r_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 2}^{(r_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 2}^{({2r})} = {f_{m\; 2}^{(r_{1})} + f_{m\; 2}^{(r_{2})}}}\end{matrix},} \right.$

where f₁ ^((r)) is a mean log likelihood ratio. (e.g., φ(z) can beapproximately:

${\phi (z)} = \left\{ {\begin{matrix}{{1 - {\frac{1}{\sqrt{4{\pi z}}}{\int_{- \infty}^{+ \infty}{\tanh \frac{u}{2}{\exp \left( {{- \left( {u - z} \right)^{2}}/\left( {4z} \right)} \right)}{du}}}}}\ } & {z > 0} \\{1,{z = 0}} & \;\end{matrix},} \right.$

where the nodes i₁ and i₂ participating in the iterative calculation aredependent on the structure of the Polar encoder);

(Let the initial value f₁ ^((r))=2/σ², where σ² is the variance ofnoise, C_(re)=8, σ²=0. f₁ ^((r)) is substituted into the iterationequation to obtain f₂ ^((r)), which is then substituted into theiteration equation to obtain f₄ ^((r)), and so on, until f₈ ^((r)) iscalculated, where f(r)=f₈ ^((r)), 0≤r≤C_(re)−1, {f(0), . . . ,f(7)}={0.04, 0.41, 0.61, 3.29, 1.00, 4.56, 5.78, 16.00}); or

initializing a function value corresponding to r as f₁ ^((r)), andobtaining a function value for each element f_(C) _(re) ^((r)) aftern1-th iteration in accordance with a second iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 3}^{({{2r} - 1})} = {f_{m\; 3}^{(r_{1})} + f_{m\; 3}^{(r_{2})} - {f_{m\; 3}^{(r_{1})}f_{m\; 3}^{(r_{2})}}}} \\{f_{2m\; 3}^{({2r})} = {f_{m\; 3}^{(r_{1})}f_{m\; 3}^{(r_{2})}}}\end{matrix},} \right.$

where f₁ ^((r)) is mutual information, where 1≤m2≤n1, 1≤m3≤n1, and r1,r2, 2r and 2r−1 are all integers larger than or equal to 0 and smallerthan or equal to C_(re)−1 (the nodes i₁ and i₂ participating in theiterative calculation are dependent on the structure of the Polarencoder);

(Let f₁ ^((r))=0.5 and C_(re)=8. f₁ ^((r)) is substituted into theiteration equation to obtain f₂ ^((r)), which is then substituted intothe iteration equation to obtain f₄ ^((r)), and so on, until f₈ ^((r))is calculated, where f(r)=f₈ ^((r)), 0≤i≤C_(re)−1, {f(0), . . . ,f(7)}={0.008, 0.152, 0.221, 0.682, 0.313, 0.779, 0.850, 0.991}).

It is to be noted that the above π₂(j) can be obtained according to atleast one of:

π₂(j)=BRO(j), where BRO( ) denotes a bit reverse ordering operationwhich includes: converting a decimal number j into a third binary number(B_(n2-1), B_(n2-2), . . . , B₀), reversing the third binary number toobtain a fourth binary number (B₀, B₁, . . . , B_(n2-1)) and convertingthe fourth binary number into a decimal number π₂(j), wheren2=log₂(R_(re)) and 0≤j≤R_(re)−1;

π₂(j)={S4, S5, S6}, where S4={0, 1, . . . , j1−1}, S5={j2, j3, j2+1,j3+1, . . . , j4, j5}, and S6 is a set of elements in {0, 1, . . . ,R_(re)−1} other than those included in S4 and S5, whereR_(re)/8≤j1≤j2≤R_(re)/3, j2≤j4≤j3≤2 R_(re)/3, j3≤j5≤R_(re)−1, j1, j2,j3, j4 and j5 are all non- negative integers, and an intersection of anytwo of S4, S5 and S6 is null; or

π₂(j)={J}, where {J} is a sequence obtained by organizing numericalresults of applying a function f(s) to row indices s of M_(or) inascending or descending order, where 0≤s≤R_(re)−1.

It is to be noted that f(s) includes at least one of:

${{f(s)} = {\sum_{{m\; 4} = 0}^{{n\; 2} - 1}{B_{m\; 4} \times 2^{\frac{m\; 4}{k}}}}},$

(B_(n2-1), B_(n2-2), . . . , B₀) is a binary representation of the indexs, where 0≤m4≤n2−1, n2=log₂(R_(re)), and k is a non-negative integer;

initializing a function value corresponding to s as f₁ ^((s)), andobtaining a function value for each element f_(R) _(re) ^((s)) aftern2-th iteration in accordance with a third iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 5}^{({{2s} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 5}^{(s_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 5}^{(s_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 5}^{({2s})} = {f_{m\; 5}^{(s_{1})} + f_{m\; 5}^{(s_{2})}}}\end{matrix},} \right.$

where f₁ ^((s)) is a mean log likelihood ratio; or

initializing a function value corresponding to s as f₁ ^((s)), andobtaining a function value for each element f_(R) _(re) ^((s)) aftern2-th iteration in accordance with a fourth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 6}^{({{2s} - 1})} = {f_{m\; 6}^{(s_{1})} + f_{m\; 6}^{(s_{2})} - {f_{m\; 6}^{(s_{1})}f_{m\; 6}^{(s_{2})}}}} \\{f_{2m\; 6}^{({2s})} = {f_{m\; 6}^{(s_{1})}f_{m\; 6}^{(s_{2})}}}\end{matrix},} \right.$

where f₁ ^((s)) is mutual information, where 1≤m5≤n2, 1≤m6≤n2, s1, s2,2s and 2s−1 are all integers larger than or equal to 0 and smaller thanor equal to R_(re)−1.

It is to be noted that, for explanations for the above π₂(j), referencecan be made to π₁(i).

It is to be noted that the above first bit sequence matrix can be, butnot limited to, a two dimensional, three dimensional ormulti-dimensional matrix. In an example where the above first bitsequence matrix is a two dimensional matrix, the above secondpredetermined transform can be embodied such that a row transformpattern or a column transform pattern for the first bit sequence matrixis the same.

It is to be noted that the first bit sequence matrix is M_(og). Thesecond bit sequence matrix is M_(vb), which is a matrix of R_(vb) rowsand C_(vb) columns. M_(og) is:

$M_{og} = {\begin{bmatrix}x_{0} & x_{1} & x_{2} & \ldots & x_{C_{vb} - 1} \\x_{C_{vb}} & x_{C_{vb} + 1} & x_{C_{vb} + 2} & \ldots & x_{{2C_{vb}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{{({R_{vb} - 1})} \times C_{vb}} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 1} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 2} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}\mspace{14mu} {or}}$$\mspace{20mu} {{M_{og} = \begin{bmatrix}x_{0} & x_{R_{vb}} & x_{2R_{vb}} & \ldots & x_{{({C_{vb} - 1})} \times R_{vb}} \\x_{1} & x_{R_{vb} + 1} & x_{{2R_{vb}} + 1} & \ldots & x_{{{({C_{vb} - 1})} \times R_{vb}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{R_{vb} - 1} & x_{{2R_{vb}} - 1} & x_{{3R_{vb}} - 1} & \ldots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}},}$

where x₀, x₁, x₂, . . . , x_(R) _(vb) _(×C) _(vb) ₋₁ is the Polarencoded bit sequence, R_(vb)×C_(vb)≥N, R_(vb) and C_(vb) are bothnon-negative integers and N is a length of the Polar encoded bitsequence.

It is to be noted that when R_(vb) is constant, C_(vb) is a minimumvalue satisfying R_(vb)×C_(vb)≥N; or when C_(vb) is constant, R_(vb) isa minimum value satisfying R_(vb)×C_(vb)≥N.

It is to be noted that the above processor 42 can further be configuredto obtain the second bit sequence matrix according to at least one of:the g-th column of M_(vb) being obtained from the π₃(g)-th column ofM_(og) by means of column permutation, where 0≤g≤C_(vb)−1,0≤π₃(g)≤C_(vb)−1, R_(vb)×C_(vb)≥N, and g and π₃(g) are both non-negativeintegers; or the h-th row of M_(vb) being obtained from the π₄(h)-th rowof M_(og) by means of row permutation, where 0≤h≤R_(vb)−1,0≤π₄(h)≤R_(vb)−1, R_(vb)×C_(vb)≥N, and h and π₄(h) are both non-negativeintegers.

It is to be noted that π₃(g) can be obtained according to at least oneof:

π₃(g)=BRO(g), where BRO( ) denotes a bit reverse ordering operationwhich includes: converting a decimal number g into a fifth binary number(B_(n3-1), B_(n3-2), . . . , B₀), reversing the fifth binary number toobtain a sixth binary number (B₀, B₁₁, . . . , B_(n3-1)) and convertingthe sixth binary number into a decimal number π₃(g), wheren3=log₂(C_(vb)) and 0≤g≤C_(vb)−1;

π₃(g)={S1, S2, S3}, where S1={0, 1, . . . , g1−1}, S2={g2, g3, g2+1,g3+1, . . . , g4, g5}, and S3 is a set of elements in {0, 1, . . . ,C_(vb)−1} other than those included in S1 and S2, whereC_(vb)/8≤g1≤g2≤C_(vb)/3, g2≤g4≤g3≤2C_(vb)/3, g3≤g5≤C_(vb)−1, g1, g2, g3,g4 and g5 are all non- negative integers, and an intersection of any twoof S1, S2 and S3 is null;

π₃(g)={G}, where {G} is a sequence obtained by organizing numericalresults of applying a function f(α) to column indices α of M_(og) inascending or descending order, where 0≤α≤C_(vb)−1;

π₃(g)={Q1, Q2, Q3}, where Q2={q1, q2, q1+1, q2+1, . . . , q3, q4},0≤q1≤q3≤(C_(vb)−1)/2, 0≤q2≤q4≤(C_(vb)−1)/2, q1, q2, q3, q4 and q5 areall non-negative integers, Q1 and Q3 are other elements in a differenceset between {0, 1, . . . , C_(vb)−1} and Q2, and an intersection of anytwo of Q1, Q2 and Q3 is null;

π₃(g) being different from a predefined sequence V1 in nV1 positions,where V1={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 13, 17, 14, 18,15, 19, 20, 24, 21, 22, 25, 26, 28, 23, 27, 29, 30, 31}, 0≤nV1≤23; or

π₃(g) being different from a predefined sequence V2 in nV2 positions,where V2={0, 1, 2, 4, 3, 5, 6, 7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20,13, 21, 14, 22, 15, 23, 24, 25, 26, 28, 27, 29, 30, 31}, 0≤nV2≤3.

It is to be noted that f(α) includes at least one of:

${{f(\alpha)} = {\sum_{{m\; 6} = 0}^{{n\; 3} - 1}{B_{m\; 6} \times 2^{\frac{m\; 6}{k}}}}},$

(B_(n3-1), B_(n3-2), . . . , B₀) is a binary representation of the indexα, where 0≤m6≤n3−1, n3=log₂(C_(vb)), and k is a non-negative integer;

initializing a function value corresponding to α as f₁ ^((α)), andobtaining a function value for each element f_(C) _(vb) ^((α)) aftern-th iteration in accordance with a fifth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 7}^{({{2\alpha} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 7}^{(\alpha_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 7}^{(\alpha_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 7}^{({2\alpha})} = {f_{m\; 7}^{(\alpha_{1})} + f_{m\; 7}^{(\alpha_{2})}}}\end{matrix},} \right.$

where f₁ ^((α)) is a mean log likelihood ratio; or

initializing a function value corresponding to s as a), and obtaining afunction value for each element f_(C) _(vb) ^((α)) after n3-th iterationin accordance with a sixth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 8}^{({{2\alpha} - 1})} = {f_{m\; 8}^{(\alpha_{1})} + f_{m\; 8}^{(\alpha_{2})} - {f_{m\; 8}^{(\alpha_{1})}f_{m\; 8}^{(\alpha_{2})}}}} \\{f_{2m\; 8}^{({2\alpha})} = {f_{m\; 8}^{(\alpha_{1})}f_{m\; 8}^{(\alpha_{2})}}}\end{matrix},} \right.$

where f₁ ^((α)) is mutual information, where 1≤m7≤n3, 1≤m8≤n3, and α1,α2, 2α and 2α−1 are all integers larger than or equal to 0 and smallerthan or equal to C_(vb)−1.

It is to be noted that π₄(h) can be obtained according to at least oneof:

π₄(h)=BRO(h), where BRO( ) denotes a bit reverse ordering operationwhich includes: converting a decimal number h into a seventh binarynumber (B_(n4-1), B_(n4-2), . . . , B₀), reversing the seventh binarynumber to obtain an eighth binary number (B₀, B₁, . . . , B_(n4-1)) andconverting the eighth binary number into a decimal number π₄(h), wheren4=log₂(R_(vb)) and 0≤h≤R_(vb)−1;

π₄(h)={S4, S5, S6}, where S4={0, 1, . . . , h1−1}, S5={h2, h3, h2+1,h3+1, . . . , h4, h5}, and S6 is a set of elements in {0, 1, . . . ,R_(vb)−1} other than those included in S4 and S5, whereR_(vb)/8≤h1≤h2≤R_(vb)/3, h2≤h4≤h3≤2R_(vb)/3, h3≤h5≤R_(vb)−1, h1, h2, h3,h4 and h5 are all non- negative integers, and an intersection of any twoof S4, S5 and S6 is null;

π₄(h)={H}, where {H} is a sequence obtained by organizing numericalresults of applying a function f(β) to row indices β of M_(og) inascending or descending order, where 0≤3≤R_(vb)−1;

π₄(h)={O1, O2, O3}, where O2={o1, o2, o1+1, o2+1, . . . , o3, o4},0≤o1≤o3≤(R_(vb)−1)/2, 0≤o2≤o4≤(R_(vb)−1)/2, o1, o2, o3, o4 and o5 areall non-negative integers, O1 and O3 are other elements in a differenceset between {0, 1, . . . , R_(vb)−1} and O2, and an intersection of anytwo of O1, O2 and O3 is null;

π₄(h) being different from a predefined sequence VV1 in nVV1 positions,where VV1={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 13, 17, 14, 18,15, 19, 20, 24, 21, 22, 25, 26, 28, 23, 27, 29, 30, 31}, 0≤nVV1≤23; or

π₄(h) being different from a predefined sequence VV2 in nVV2 positions,where VV2={0, 1, 2, 4, 3, 5, 6, 7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20,13, 21, 14, 22, 15, 23, 24, 25, 26, 28, 27, 29, 30, 31}, 0≤nVV2≤3.

It is to be noted that f(β) includes at least one of:

${{f(\beta)} = {\sum_{{m\; 9} = 0}^{{n\; 4} - 1}{B_{m\; 9} \times 2^{\frac{m\; 9}{k}}}}},$

(B_(n4-1), B_(n4-2), . . . , B₀) is a binary representation of the indexβ, where 0≤m9≤n4−1, n4=log₂(R_(vb)), and k is a non-negative integer;

initializing a function value corresponding to β as f₁ ^((β)), andobtaining a function value for each element f_(R) _(vb) ^((β)) aftern4-th iteration in accordance with a seventh iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 10}^{({{2\beta} - 1})} = {\phi^{- 1}\left( {1 - {\left\lbrack {1 - {\phi \left( f_{m\; 10}^{(\beta_{1})} \right)}} \right\rbrack \left\lbrack {1 - {\phi \left( f_{m\; 10}^{(\beta_{2})} \right)}} \right\rbrack}} \right)}} \\{f_{2m\; 10}^{({2\beta})} = {f_{m\; 10}^{(\beta_{1})} + f_{m\; 10}^{(\beta_{2})}}}\end{matrix},} \right.$

where f₁ ^((β)) is a mean log likelihood ratio; or

initializing a function value corresponding to β as f₁ ^((β)), andobtaining a function value for each element f_(R) _(vb) ^((β)) aftern4-th iteration in accordance with an eighth iteration equation:

$\left\{ {\begin{matrix}{f_{2m\; 11}^{({{2\beta} - 1})} = {f_{m\; 11}^{(\beta_{1})} + f_{m\; 11}^{(\beta_{2})} - {f_{m\; 11}^{(\beta_{1})}f_{m\; 11}^{(\beta_{2})}}}} \\{f_{2m\; 11}^{({2\beta})} = {f_{m\; 11}^{(\beta_{1})}f_{m\; 11}^{(\beta_{2})}}}\end{matrix},} \right.$

where f₁ ^((β)) is mutual information, where 1≤m10≤n4, 1≤m11≤n4, and β1,β2, 2β and 2β−1 are all integers larger than or equal to 0 and smallerthan or equal to R_(vb)−1.

It is to be noted that, for explanations for π₃(g) and π₄(h), referencecan be made to π₁(i) and descriptions thereof will be omitted here.

In an embodiment of the present disclosure, the above first transformmodule can further be configured to select a predetermined number ofindices based on M_(re) row by row, column by column or diagonal bydiagonal, as M_index.

It is to be noted that the operation of selecting the predeterminednumber of indices from M_(re) column by column includes: selecting π_(p)indices from the p-th column of M_(re), where Σ_(p=1) ^(C) ^(re)K_(p)=K, p is an integer, and 1≤p≤C_(re). The operation of selecting thepredetermined number of indices from M_(re) row by row includes:selecting π_(q) indices from the q-th row of M_(re), where Σ_(q=1) ^(R)^(re) K_(q)=K, q is an integer, and 1≤q≤R_(re). The operation ofselecting the predetermined number of indices from M_(re) diagonal bydiagonal includes: selecting K_(δ) indices from the δ-th diagonal ofM_(re), where

${{{\sum_{\delta = {{- {\min {({R_{re},C_{re}})}}} + 1}}^{{\max {({R_{re},C_{re}})}} - 1}K_{\delta}} = K},}\;$

δ is an integer, and −min(R_(re), C_(re))+≤6≤max(R_(re), C_(re))−1,where min(R_(re), C_(re)) denotes the smaller of R_(re) and C_(re), andmax(R_(re), C_(re)) denotes the larger of R_(re) and C_(re).

It is to be noted that the operation of selecting the predeterminednumber of indices from M_(re) column by column includes at least one of:selecting K_(ic1) indices from the 1^(st), 2^(nd)C₁-th columns ofM_(re), where Σ_(ic1=1) ^(C) ¹ K_(ic1)=K, 1≤ic1≤C₁, 1≤C≤C_(re), and ic1and C₁ are integers; selecting K_(ic2) indices from the C₂-th,(C₂+1)-th, . . . , C₃-th columns of M_(re), where Σ_(ic2=C) ₂ ^(C) ³K_(ic2)=K, C₂≤ic2≤C₃, 1≤C₂≤C₃≤C_(re), and ic2, C₂ and C₃ are integers;or selecting K_(ic3) indices from the C₄-th, (C₄+1)-th, . . . ,C_(re)-th columns of M_(re), where Σ_(ic3=C) ₄ ^(C) ^(re) K_(ic3)=K,C₄≤ic3≤C_(re), 1≤C₄≤C_(re), and ic3 and C₄ are integers.

It is to be noted that the operation of selecting the predeterminednumber of indices from M_(re) row by row includes at least one of:selecting K_(ir1) indices from the 1^(st), 2^(nd), . . . , R₁-th rows ofM_(re), where Σ_(ir1=1) ^(R) ¹ K_(ir1)=K, 1≤ir1≤R, 1≤R₁≤R_(re), and ir1and R₁ are integers; selecting K_(ir2) indices from the R₂-th,(R₂+1)-th, . . . , R₃-th rows of M_(re), where Σ_(ir2=R) ₂ ^(R) ³K_(ir2)=K, R₂≤ir2≤R₃, 1≤R₂≤R₃≤R_(re), and ir2, R₂ and R₃ are integers;or selecting K_(ir3) indices from the R₄-th, (R₄+1)-th, . . . ,R_(re)-th rows of M_(re), where Σ_(ir3=R) ₄ ^(R) ^(re) K_(p)=K,1≤R₄≤R_(re), and ir3 and R₄ are integers.

It is to be noted that the operation of selecting the predeterminednumber of indices from M_(re) diagonal by diagonal includes at least oneof: selecting K_(id1) indices from the (−min(R_(re), C_(re))+1)-th,(−min(R_(re), C_(re))+2)-th, . . . , D₁-th diagonals of M_(re), whereΣ_(id1=−min(R) _(re) _(, C) _(re) ₎₊₁ ^(D) ¹ K_(id1)=K, −min(R_(re),C_(re))+1≤D₁≤max(R_(re), C_(re))−1, and id1 and D₁ are integers;selecting K_(id2) indices from the D₂-th, (D₂+1)-th, . . . , D₃-thdiagonals of M_(re), where Σ_(id2=D) ₂₁ ^(D) ³ K_(id2)=K, −min(R_(re),C_(re))+1≤D₂≤D₃≤max(R_(re), C_(re))−1, and id2, D₂ and D₃ are integers;and selecting K_(id3) indices from the D₄-th, (D₄+1)-th, . . . ,(max(R_(re), C_(re))−1)-th diagonals of M_(re), where

${{{\sum_{{{id}\; 3} = D_{4}}^{{\max {({R_{re},C_{re}})}} - 1}K_{{id}\; 3}} = K},}\;$

−min(R_(re), C_(re))+1≤D₄≤max(R_(re), C_(re))−1, and id3 and D₄ areintegers, where min(R_(re), C_(re)) denotes the smaller of R_(re) andC_(re), and max(R_(re), C_(re)) denotes the larger of R_(re) and C_(re).

It is to be noted that, when the predetermined number of indices areselected from M_(re) row by row, column by column or diagonal bydiagonal, each index corresponding to a non-transmitted bit sequence ina second bit sequence matrix is skipped. The second bit sequence matrixis obtained from a first bit sequence matrix by using a secondpredetermined transform. The first bit sequence matrix is formed fromthe Polar encoded bit sequence. The second predetermined transformincludes row permutation or column permutation.

It is to be noted that the above processor 42 can further be configuredto select T bits based on the second bit sequence matrix row by row,column by column or diagonal by diagonal, as the bit sequence to betransmitted.

It is to be noted that the above processor 42 can further be configuredto select T bits based on the second bit sequence matrix row by row,column by column or diagonal by diagonal, from a starting position t inthe second bit sequence matrix. When the selection reaches the first orlast bit in the second bit sequence matrix, it continues with the lastor first bit in the second bit sequence matrix, where 1≤t≤R_(vb)×C_(vb).

It is to be noted that the above processor 42 can further be configuredto select the 1^(st) to T-th bits or the (N−T+1)-th to N-th bits fromthe second bit sequence matrix column by column, when T is smaller thanor equal to a length N of the Polar encoded bit sequence; select the1^(st) to T-th bits or the (N−T+1)-th to N-th bits from the second bitsequence matrix row by row, when T is smaller than or equal to thelength N of the Polar encoded bit sequence; select the 1^(st) to T-thbits or the (N−T+1)-th to N-th bits from the second bit sequence matrixdiagonal by diagonal, when T is smaller than or equal to the length N ofthe Polar encoded bit sequence; select, when T is larger than the lengthN of the Polar encoded bit sequence, T bits row by row, column by columnor diagonal by diagonal, from the t-th bit in the second bit sequencematrix. When the selection reaches the first or last bit in the secondbit sequence matrix, it continues with the last or first bit in thesecond bit sequence matrix, where 1≤t≤R_(vb)×C_(vb) and N is anon-negative integer.

It is to be noted that the operation of selecting T bits from the secondbit sequence matrix column by column includes at least one of: selectingT_(ie1) bits from the 1^(st), 2^(nd), . . . , E₁-th columns, whereΣ_(ie1=1) ^(E) ¹ T_(ie1)=T, 1≤E₁≤C_(vb), and ie1 and E₁ are integers;selecting T_(ie2) bits from the E₂-th, (E₂+1)-th, . . . , E₃-th columns,where Σ_(ie2=E) ₂ ^(E) ³ T_(ie2)=T, 1≤E₂≤E₃≤C_(re), and ie2, E₂ and E₃are integers; or selecting T_(ie3) bits from the E₄-th, (E₄+1)-th, . . ., E_(vb)-th columns, where Σ_(ie3=E) ₄ ^(C) ^(vb) T_(ie3)=T,1≤E₄≤C_(vb), and ie3 and E₄ are integers.

It is to be noted that the operation of selecting T bits from the secondbit sequence matrix row by row includes at least one of: selecting Tinbits from the 1^(st), 2^(nd), . . . , F₁-th rows, where Σ_(if1=1) ^(F) ¹T_(if1)=T, 1≤F₁≤R_(vb), and if1 and F₁ are integers; selecting T_(if2)bits from the F₂-th, (F₂+1)-th, . . . , F₃-th rows, where Σ_(if2=F) ₂^(F) ³ T_(if2)=T, 1≤F₃≤R_(vb), and if2, F₂ and F₃ are integers; orselecting T_(if3) bits from the F₄-th, (F₄+1)-th, . . . , R_(vb)-throws, where Σ_(if3=F) ₄ ^(R) ^(vb) T_(if3)=T, 1≤F₄R_(vb), and if3 and F₄are integers.

It is to be noted that the operation of selecting T bits from the secondbit sequence matrix diagonal by diagonal includes at least one of:selecting T_(ig1) bits from the (−min(R_(vb), C_(vb))+1)-th,(−min(R_(vb), C_(vb))+2)-th, . . . , G₁-th diagonals, whereΣ_(ig1=−min(R) _(vb) _(, C) _(vb) ₎₊₁ ^(G) ¹ T_(ig1)=T, −min(R_(vb),C_(vb))+≤G₁≤max(R_(vb), C_(vb))−1, and ig1 and G₁ are integers;selecting K_(ig2) bits from the G₂-th, (G₂+1)-th, . . . , G₃-thdiagonals, where Σ_(ig2=G) ₂ ^(G) ³ T_(ig2)=T, −min(R_(vb),C_(vb))+1≤G₂≤G₃≤max(R_(vb), C_(vb))−1, and ig2, G₂ and G₃ are integers;or selecting K_(id3) bits from the G₄-th, (G₄+1)-th, . . . ,(max(R_(vb), C_(vb))−1)-th diagonals, where

${{{\sum_{{{ig}\; 3} = G_{4}}^{{\max {({R_{vb},C_{vb}})}} - 1}T_{{ig}\; 3}} = T},}\;$

−min(R_(vb), C_(vb))+1≤G₄≤max(R_(vb), C_(vb))−1, and ig3 and G₄ areintegers.

It is to be noted that the above device can be, but not limited to aterminal or a network device such as a base station.

Embodiment 4

According to an embodiment of the present disclosure, a storage mediumis also provided. The storage medium stores a program which, whenexecuted, performs any of the above described methods.

According to an embodiment of the present disclosure, the above storagemedium can be configured to store program codes for performing the stepsof the method described above in connection with Embodiment 1.

According to an embodiment of the present disclosure, the above storagemedium may include, but not limited to, a USB disk, a Read-Only Memory(ROM), a Random Access Memory (RAM), a mobile hard disk, a magneticdisk, an optical disc, or other mediums capable of storing programcodes.

According to an embodiment of the present disclosure, a processor isprovided. The processor is configured to execute a program forperforming the steps of any of the above described methods.

According to an embodiment of the present disclosure, the above programis configured to perform the steps of the method described above inconnection with Embodiment 1.

For detailed examples of this embodiment, reference can be made to thoseexamples described in connection with the above and optional embodimentsand description thereof will be omitted here.

In the following, the present disclosure will be further explained withreference to the examples, such that the present disclosure can bebetter understood.

Example 1

The following numerical values are provided for the purpose ofillustration. For other situations, reference can be made to thefollowing operation steps.

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the firstbit sequence is K=40 and the length of the bit sequence to betransmitted is T=100. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is as follows.

(1) The number R_(re) of rows of the index matrix M_(re) needs to beselected as a minimum value satisfying R_(re)×C_(re)≥N. According to theabove assumptions, C_(re)=³² and N=128, then R_(re)=⁴. It is assumedthat the indices in the index matrix M_(og) are arranged row by row:

$\begin{matrix}{M_{or} = \begin{bmatrix}0 & 1 & 2 & \cdots & {C_{re} - 1} \\C_{re} & {C_{re} + 1} & {C_{re} + 2} & \cdots & {{2C_{re}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\{\left( {R_{re} - 1} \right) \times C_{re}} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 1} & {{\left( {R_{re} - 1} \right) \times C_{re}} + 2} & \cdots & {{R_{re} \times C_{re}} - 1}\end{bmatrix}} \\{= \begin{bmatrix}0 & 1 & 2 & \cdots & 31 \\32 & 33 & 34 & \cdots & 63 \\64 & 65 & 66 & \ddots & 95 \\96 & 97 & 98 & \cdots & 127\end{bmatrix}}\end{matrix}$

(2) If the index matrix M_(re) is obtained from the index matrix M_(or)by means of column permutation, e.g., by mapping the π₁(i)-th column ofthe index matrix M_(or) to the i-th column of the index matrix M_(re) bymeans of column permutation. The indices in π₁(i) are arranged inascending order of numerical results obtained based on a function. Ifthe function is expressed as

${{f(i)} = {\sum_{m = 0}^{n - 1}{B_{m} \times 2^{\frac{m}{k}}}}}\;$

k=4, then {f(0), . . . , f(31)}={0, 1, 1.19, 2.19, 1.41, 2.41, 2.60,3.60, 1.68, 2.68, 2.87, 3.87, 3.10, 4.10, 4.29, 5.29, 2.00, 3.00, 3.19,4.19, 3.41, 4.41, 4.60, 5.60, 3.68, 4.68, 4.87, 0.87, 5.10, 6.10, 6.29,7.29}. f(0), . . . , f(31) are arranged in ascending order to obtain acolumn permutation pattern π₁(i)={0, 1, 2, 4, 8, 16, 3, 5, 6, 9, 10, 17,12, 18, 20, 7, 24, 11, 13, 19, 14, 21, 22, 25, 26, 28, 15, 23, 27, 29,30, 31}. Accordingly, the column having an index of 0 in the indexmatrix M_(or) is the column having an index of 0 in the index matrixM_(re), the column having an index of 1 in the index matrix M_(or) isthe column having an index of 1 in the index matrix M_(re), the columnhaving an index of 2 in the index matrix M_(or) is the column having anindex of 2 in the index matrix M_(re), the column having an index of 4in the index matrix M_(or) is the column having an index of 3 in theindex matrix M_(re), the column having an index of 8 in the index matrixM_(or) is the column having an index of 4 in the index matrix M_(re),and so on.

(3) The bit sequence matrix M_(vb) is obtained from the bit sequencematrix M_(og) by means of column permutation, e.g., by mapping theπ₂(i)-th column of the bit sequence matrix M_(og) to the i-th column ofthe bit sequence matrix M_(vb) by means of column permutation. Here,π₂(i)=BRO(i), and the column permutation pattern is 2(i)⁼{0, 16, 8, 24,4, 20, 12, 28, 2, 18, 10, 26, 6, 22, 14, 30, 1, 17, 9, 25, 5, 21, 13,29, 3, 19, 11, 27, 7, 23, 15, 31}. Accordingly, the column having anindex of 0 in the bit sequence matrix M_(og) is the column having anindex of 0 in the bit sequence matrix M_(vb), the column having an indexof 16 in the bit sequence matrix M_(og) is the column having an index of1 in the bit sequence matrix M_(vb), the column having an index of 8 inthe bit sequence matrix M_(og) is the column having an index of 2 in thebit sequence matrix M_(vb), and so on.

(4) The first T=100 bits are selected from the bit sequence matrixM_(vb) column by column to form a bit sequence to be transmitted, whichis {y₀, y₃₂, y₆₄, y₉₆, y₁₆, y₄₈, y₈₀, y₁₁₂, . . . , y₂₃, y₅₅, y₈₇,y₁₁₉}.

(5) K=40 indices in total are selected from the index matrix M_(re) rowby row to form the index sequence M_index. It is to be noted that,during the selection of the indices, each index corresponding to anon-transmitted bit sequence is skipped. That is, the selection is madefrom the indices corresponding to the bit sequence to be transmitted asoutputted from an encoder in the step (4).

(6) After an input bit sequence having a length of K is mapped toencoder positions indicated by the index sequence M_index, Polarencoding can be applied to obtain an encoded bit sequence having alength of N=128. The bits determined in the step (4) are organized intoa bit sequence to be transmitted, for transmission from a transmitter.

Example 2

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=100. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 1 in that, in the step (4), the last T=100 bits are selectedfrom the bit sequence matrix M_(vb) column by column to form the bitsequence to be transmitted, which is {y₈, y₂₄, y₄₀, y₅₆, y₇₂, y₈₈, y₁₀₄,y₁₂₀, . . . , y₁₅, y₃₁, y₄₇, y₆₃, y₇₉, y₉₅, y₁₁₁, y₁₂₇}.

Example 3

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=150. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 1 in that, in the step (4), T=130 bits are selected from the bitsequence matrix M_(vb) row by row, starting from the first element inthe bit sequence matrix M_(vb). When the selection reaches the last bity₁₂₇ in the buffer or in the bit sequence matrix M_(vb), it continueswith the first bit y₀ of the bit sequence matrix M_(vb). The resultingbit sequent to be transmitted is {y₀, y₁, y₂, . . . , y₁₂₇, y₀, y₁, y₂}.

Example 4

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=150. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 3 in that, in the step (4), T=130 bits are selected from the bitsequence matrix M_(vb) row by row, starting from the last element in thebit sequence matrix M_(vb). When the selection reaches the first bit y₀in the buffer or in the bit sequence matrix M_(vb), it continues withthe last bit y₁₂₇ of the bit sequence matrix M_(vb). The resulting bitsequent to be transmitted is {y₀, y₁, y₂, . . . , y₁₂₇, y₁₂₇, y₁₂₆,y₁₂₅}.

Example 5

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=100. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 1 in that, the input bit sequence having the length of K=40 ismapped to the encoder positions using Gaussian approximation, densityevolution, PW sequence, FRANK sequence, or other schemes. Details of theoperations will be omitted here.

Example 6

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=100. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 2 in that, the input bit sequence having the length of K=40 ismapped to the encoder positions using Gaussian approximation, densityevolution, PW sequence, FRANK sequence, or other schemes. Details of theoperations will be omitted here.

Example 7

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=130. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 3 in that, the input bit sequence having the length of K=40 ismapped to the encoder positions using Gaussian approximation, densityevolution, PW sequence, FRANK sequence, or other schemes. Details of theoperations will be omitted here.

Example 8

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=130. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 4 in that, the input bit sequence having the length of K=40 ismapped to the encoder positions using Gaussian approximation, densityevolution, PW sequence, FRANK sequence, or other schemes. Details of theoperations will be omitted here.

Example 9

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=100. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 1 in that a different rate matching scheme is used. Details ofthe operations will be omitted here.

Example 10

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=100. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 2 in that a different rate matching scheme is used. Details ofthe operations will be omitted here.

Example 11

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=130. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 3 in that a different rate matching scheme is used. Details ofthe operations will be omitted here.

Example 12

It is assumed that the number of columns in each of the index matrixM_(or), the index matrix M_(re), the bit sequence matrix M_(vb) and thebit sequence matrix M_(og) is fixed to be 32. The length of the inputbit sequence is K=40 and the length of the bit sequence to betransmitted is T=130. Polar encoding having a mother code length of 128is applied. In particular, the encoding process is different fromExample 4 in that a different rate matching scheme is used. Details ofthe operations will be omitted here.

It can be appreciated by those skilled in the art that theabove-described modules or steps of the present disclosure can beimplemented by a general purpose computing device, and can becentralized at one single computing device or distributed over a networkof multiple computing devices. Optionally, they can be implemented bymeans of computer executable program codes, which can be stored in astorage device and executed by one or more computing devices. In somecases, the steps shown or described herein may be performed in an orderdifferent from the one described above. Alternatively, they can beimplemented separately in individual integrated circuit modules, or oneor more of the modules or steps can be implemented in one singleintegrated circuit module. Thus, the present disclosure is not limitedto any particular hardware, software, and combination thereof.

The foregoing is merely illustrative of the examples of the presentdisclosure and is not intended to limit the present disclosure. Variouschanges and modifications may be made by those skilled in the art. Anymodifications, equivalent alternatives or improvements that are madewithout departing from the spirits and principles of the presentdisclosure are to be encompassed by the scope of the present disclosure.

INDUSTRIAL APPLICABILITY

With the present disclosure, a first bit sequence having a length of Kbits is mapped to a specified position based on M_index to obtain asecond bit sequence. Polar encoding is applied to the second bitsequence to obtain a Polar encoded bit sequence. T bits are selectedbased on the Polar encoded bit sequence as a bit sequence to betransmitted. That is, the present disclosure provides a method fordetermining a bit sequence to be transmitted, capable of solving theproblem in the related art associated with lack of a sequencedetermination scheme in the 5G New RAT.

1. A method for channel coding, comprising: mapping a first bit sequencehaving a length of K bits to a second bit sequence based on an indexindicating a first permutation pattern; applying Polar encoding to thesecond bit sequence to obtain a Polar encoded bit sequence; forming afirst bit sequence matrix based on the Polar encoded bit sequence;determining a second bit sequence matrix by applying a secondpermutation pattern to the first bit sequence matrix; and selecting Tbits based on the second bit sequence matrix, where K and T are bothnon-negative integers. 2-10. (canceled)
 11. The method of claim 1,wherein the first bit sequence matrix is M_(og), and$M_{og} = {\begin{bmatrix}x_{0} & x_{1} & x_{2} & \cdots & x_{C_{vb} - 1} \\x_{C_{vb}} & x_{C_{vb} + 1} & x_{C_{vb} + 2} & \cdots & x_{{2C_{vb}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{{({R_{vb} - 1})} \times C_{vb}} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 1} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 2} & \cdots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}\mspace{14mu} {or}}$ ${M_{og} = \begin{bmatrix}x_{0} & x_{R_{vb}} & x_{2R_{vb}} & \cdots & x_{{({C_{vb} - 1})} \times R_{vb}} \\x_{1} & x_{R_{vb} + 1} & x_{{2R_{vb}} + 1} & \cdots & x_{{{({C_{vb} - 1})} \times R_{vb}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{R_{vb} - 1} & x_{{2R_{vb}} - 1} & x_{{3R_{vb}} - 1} & \cdots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}},$ where x₀, x₁, x₂, . . . , x_(R) _(vb) _(×C) _(vb) ₋₁ isthe Polar encoded bit sequence, R_(vb) and C_(vb) being bothnon-negative integers. 12-13. (canceled)
 14. The method of claim 1,wherein the second permutation pattern comprises a row or a column beingsame as a predefined sequence V2 in all positions, where V2={0, 1, 2, 4,3, 5, 6, 7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20, 13, 21, 14, 22, 15,23, 24, 25, 26, 28, 27, 29, 30, 31}. 15-23. (canceled)
 24. The method ofclaim 1, wherein said selecting T bits based on the second bit sequencematrix as comprises: selecting T bits column by column from the secondbit sequence matrix.
 25. The method of claim 1, wherein said selecting Tbits based on the second bit sequence matrix comprises: performing aselection of T bits from a starting position t in the second bitsequence matrix, wherein the selection continues with a first bit in thesecond bit sequence matrix upon reaching a last bit in the second bitsequence matrix, where 1≤t. 26-29. (canceled)
 30. The method of claim 1,wherein the first bit sequence matrix comprises 32 columns. 31-33.(canceled)
 34. A device for channel coding, comprising: a processor; anda memory including processor executable code, wherein the processorexecutable code upon execution by the processor configures the processorto: map a first bit sequence having a length of K bits to a second bitsequence based on an index indicating a first permutation pattern; applyPolar encoding to the second bit sequence to obtain a Polar encoded bitsequence; form a first bit sequence matrix based on the Polar encodedbit sequence; determine a second bit sequence matrix by applying asecond permutation pattern to the first bit sequence matrix; and selectT bits based on the second bit sequence matrix, where K and T are bothnon-negative integers. 35-38. (canceled)
 39. The device of claim 34,wherein the first bit sequence Matrix is M_(og), and$M_{og} = {\begin{bmatrix}x_{0} & x_{1} & x_{2} & \cdots & x_{C_{vb} - 1} \\x_{C_{vb}} & x_{C_{vb} + 1} & x_{C_{vb} + 2} & \cdots & x_{{2C_{vb}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{{({R_{vb} - 1})} \times C_{vb}} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 1} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 2} & \cdots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}\mspace{14mu} {or}}$ ${M_{og} = \begin{bmatrix}x_{0} & x_{R_{vb}} & x_{2R_{vb}} & \cdots & x_{{({C_{vb} - 1})} \times R_{vb}} \\x_{1} & x_{R_{vb} + 1} & x_{{2R_{vb}} + 1} & \cdots & x_{{{({C_{vb} - 1})} \times R_{vb}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{R_{vb} - 1} & x_{{2R_{vb}} - 1} & x_{{3R_{vb}} - 1} & \cdots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}},$ where x₀, x₁, x₂, . . . , x_(R) _(vb) _(×C) _(vb) ₋₁ isthe Polar encoded bit sequence, R_(vb) and C_(vb) being bothnon-negative integers.
 40. The device of claim 34, wherein the secondpermutation pattern comprises a row or a column being same as apredefined sequence V2 in all positions, where V2={0, 1, 2, 4, 3, 5, 6,7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20, 13, 21, 14, 22, 15, 23, 24, 25,26, 28, 27, 29, 30, 31}.
 41. The device of claim 34, wherein theprocessor executable code upon execution by the processor configures theprocessor to select T bits column by column from the second bit sequencematrix.
 42. The device of claim 34, wherein the processor executablecode upon execution by the processor configures the processor to performa selection of T bits from a starting position t in the second bitsequence matrix, wherein the selection continues with a first bit in thesecond bit sequence matrix upon reaching a last bit in the second bitsequence matrix, wherein t>=1.
 43. The device of claim 34, wherein thefirst bit sequence matrix comprises 32 columns.
 44. A non-transitorystorage medium having code stored thereon, the code upon execution by aprocessor, causing the processor to implement a method that comprises:mapping a first bit sequence having a length of K bits to a second bitsequence based on an index indicating a first permutation pattern;applying Polar encoding to the second bit sequence to obtain a Polarencoded bit sequence; forming a first bit sequence matrix based on thePolar encoded bit sequence; determining a second bit sequence matrix byapplying a second permutation pattern to the first bit sequence matrix;selecting T bits based on the second bit sequence matrix, where K and Tare both non-negative integers.
 45. The non-transitory storage medium ofclaim 44, wherein the first bit sequence Matrix is M_(og), and$M_{og} = {\begin{bmatrix}x_{0} & x_{1} & x_{2} & \cdots & x_{C_{vb} - 1} \\x_{C_{vb}} & x_{C_{vb} + 1} & x_{C_{vb} + 2} & \cdots & x_{{2C_{vb}} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{{({R_{vb} - 1})} \times C_{vb}} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 1} & x_{{{({R_{vb} - 1})} \times C_{vb}} + 2} & \cdots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}\mspace{14mu} {or}}$ ${M_{og} = \begin{bmatrix}x_{0} & x_{R_{vb}} & x_{2R_{vb}} & \cdots & x_{{({C_{vb} - 1})} \times R_{vb}} \\x_{1} & x_{R_{vb} + 1} & x_{{2R_{vb}} + 1} & \cdots & x_{{{({C_{vb} - 1})} \times R_{vb}} + 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\x_{R_{vb} - 1} & x_{{2R_{vb}} - 1} & x_{{3R_{vb}} - 1} & \cdots & x_{{R_{vb} \times C_{vb}} - 1}\end{bmatrix}},$ where x₀, x₁, x₂, . . . , x_(R) _(vb) _(×C) _(vb) ₋₁ isthe Polar encoded bit sequence, R_(vb) and C_(vb) being bothnon-negative integers.
 46. The non-transitory storage medium of claim44, wherein the second permutation pattern comprises a row or a columnbeing same as a predefined sequence V2 in all positions, where V2={0, 1,2, 4, 3, 5, 6, 7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20, 13, 21, 14, 22,15, 23, 24, 25, 26, 28, 27, 29, 30, 31}.
 47. The non-transitory storagemedium of claim 44, wherein said selecting T bits based on the secondbit sequence matrix: selecting T bits column by column from the secondbit sequence matrix.
 48. The non-transitory storage medium of claim 44,wherein the method further comprises: performing a selection of T bitsfrom a starting position t in the second bit sequence matrix, whereinthe selection continues with a first bit in the second bit sequencematrix upon reaching a last bit in the second bit sequence matrix,wherein t>=1.
 49. The non-transitory storage medium of claim 44, whereinthe first bit sequence matrix comprises 32 columns.